Hyperbolic cosecant: Integration (formula 01.23.21.0153)

Csch

$Mathematica Notation$

Elementary Functions

Csch[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving hyperbolic functions

Involving sinh and cosh

http://functions.wolfram.com/01.23.21.0153.01

Input Form

Integrate[Csch[z]/Sqrt[a Cosh[z]^2 + b Cosh[z] Sinh[z] + c Sinh[z]^2], z] == (2 Sqrt[2] (1 + Cosh[z]) ((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2]) (EllipticPi[(Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]))/ (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4])), ArcSin[Sqrt[((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]) (-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] + Tanh[z/2]))/ ((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]) (-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] + Tanh[z/2]))]], -(((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 3]) (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]))/ ((-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] + Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 3]) (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4])))] + EllipticPi[(Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4])/ (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]), ArcSin[Sqrt[((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]) (-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] + Tanh[z/2]))/ ((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]) (-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] + Tanh[z/2]))]], -(((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 3]) (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]))/ ((-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] + Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 3]) (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4])))] Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2]) + EllipticF[ArcSin[Sqrt[((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]) (-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] + Tanh[z/2]))/((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]) (-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] + Tanh[z/2]))]], -(((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 3]) (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]))/ ((-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] + Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 3]) (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4])))] Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] (-1 + Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2]^2)) Sqrt[(a - c + (a + c) Cosh[2 z] + b Sinh[2 z])/(1 + Cosh[z])^2] (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Tanh[z/2]) Sqrt[((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2]) (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 3] - Tanh[z/2]))/((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 3]) (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Tanh[z/2]))] Sqrt[((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]) (-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] + Tanh[z/2]))/((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]) (-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] + Tanh[z/2]))] (-Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4] + Tanh[z/2]))/(Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]) Sqrt[a - c + (a + c) Cosh[2 z] + b Sinh[2 z]] Sqrt[Sech[z/2]^4 (a - c + (a + c) Cosh[2 z] + b Sinh[2 z])] Sqrt[((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2]) (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4] - Tanh[z/2]))/((Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 1] - Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 4]) (Root[a + 2 b #1 + 2 a #1^2 + 4 c #1^2 + 2 b #1^3 + a #1^4 & , 2] - Tanh[z/2]))])

Standard Form

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</msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Π </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mo> √ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ❘ </mo> <mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mrow> <mi> Π </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mo> √ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ❘ </mo> <mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> F </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mo> √ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ❘ </mo> <mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mfrac> <mrow> <mi> a </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> √ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> √ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <msup> <mi> sech </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> c </mi> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> √ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 4 </mn> </mrow> <mo> ] </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Root </mi> <mo> [ </mo> <mrow> <mrow> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> #1 </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> #1 </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> & </mo> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ] </mo> </mrow> <mo> - </mo> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <csch /> <ci> z </ci> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <cosh /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <sinh /> <ci> z </ci> </apply> <apply> <cosh /> <ci> z </ci> </apply> </apply> 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Date Added to functions.wolfram.com (modification date)

2002-12-18