Generalized hypergeometric function 2F3: Series representations (formula 07.26.06.0008)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]

Series representations

Asymptotic series expansions

Expansions for any z in exponential form

Case of simple poles

http://functions.wolfram.com/07.26.06.0008.01

Input Form

HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] \[Proportional] (((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]] Gamma[-Subscript[a, 1] + Subscript[a, 2]])/ (Gamma[-Subscript[a, 1] + Subscript[b, 1]] Gamma[-Subscript[a, 1] + Subscript[b, 2]] Gamma[-Subscript[a, 1] + Subscript[b, 3]] Gamma[Subscript[a, 2]])) (1 + (Subscript[a, 1] (1 + Subscript[a, 1] - Subscript[b, 1]) (1 + Subscript[a, 1] - Subscript[b, 2]) (1 + Subscript[a, 1] - Subscript[b, 3]))/(z (1 + Subscript[a, 1] - Subscript[a, 2])) + (1/(2 z^2 (1 + Subscript[a, 1] - Subscript[a, 2]) (2 + Subscript[a, 1] - Subscript[a, 2]))) (Subscript[a, 1] (1 + Subscript[a, 1]) (1 + Subscript[a, 1] - Subscript[b, 1]) (2 + Subscript[a, 1] - Subscript[b, 1]) (1 + Subscript[a, 1] - Subscript[b, 2]) (2 + Subscript[a, 1] - Subscript[b, 2]) (1 + Subscript[a, 1] - Subscript[b, 3]) (2 + Subscript[a, 1] - Subscript[b, 3])) + \[Ellipsis]))/(-z)^Subscript[a, 1] + (((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]] Gamma[Subscript[a, 1] - Subscript[a, 2]])/ (Gamma[-Subscript[a, 2] + Subscript[b, 1]] Gamma[-Subscript[a, 2] + Subscript[b, 2]] Gamma[-Subscript[a, 2] + Subscript[b, 3]] Gamma[Subscript[a, 1]])) (1 + (Subscript[a, 2] (1 + Subscript[a, 2] - Subscript[b, 1]) (1 + Subscript[a, 2] - Subscript[b, 2]) (1 + Subscript[a, 2] - Subscript[b, 3]))/(z (1 - Subscript[a, 1] + Subscript[a, 2])) + (1/(2 z^2 (1 - Subscript[a, 1] + Subscript[a, 2]) (2 - Subscript[a, 1] + Subscript[a, 2]))) (Subscript[a, 2] (1 + Subscript[a, 2]) (1 + Subscript[a, 2] - Subscript[b, 1]) (2 + Subscript[a, 2] - Subscript[b, 1]) (1 + Subscript[a, 2] - Subscript[b, 2]) (2 + Subscript[a, 2] - Subscript[b, 2]) (1 + Subscript[a, 2] - Subscript[b, 3]) (2 + Subscript[a, 2] - Subscript[b, 3])) + \[Ellipsis]))/(-z)^Subscript[a, 2] + ((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]])/ (2 Sqrt[Pi] Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]])) (-z)^((1/2) (1/2 + Subscript[a, 1] + Subscript[a, 2] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3])) (E^(I (2 Sqrt[-z] + (1/2) Pi (1/2 + Subscript[a, 1] + Subscript[a, 2] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]))) (1 - Subscript[d, 1]/Sqrt[-z] + Subscript[d, 2]/z + \[Ellipsis]) + (1 + Subscript[d, 1]/Sqrt[-z] + Subscript[d, 2]/z + \[Ellipsis])/ E^(I (2 Sqrt[-z] + (1/2) Pi (1/2 + Subscript[a, 1] + Subscript[a, 2] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3])))) /; (Abs[z] -> Infinity) && Subscript[d, 1] == (1/16) (I (-3 + 12 Subscript[a, 1]^2 + 12 Subscript[a, 2]^2 + 8 Subscript[b, 1] - 4 Subscript[b, 1]^2 + 8 Subscript[b, 2] + 8 Subscript[b, 1] Subscript[b, 2] - 4 Subscript[b, 2]^2 + 8 Subscript[a, 1] (-1 + Subscript[a, 2] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) + 8 Subscript[b, 3] + 8 Subscript[b, 1] Subscript[b, 3] + 8 Subscript[b, 2] Subscript[b, 3] - 4 Subscript[b, 3]^2 - 8 Subscript[a, 2] (1 + Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3]))) && Subscript[d, 2] == (1/512) (-15 + 144 Subscript[a, 1]^4 + 144 Subscript[a, 2]^4 + 16 Subscript[b, 1] + 56 Subscript[b, 1]^2 - 64 Subscript[b, 1]^3 + 16 Subscript[b, 1]^4 + 16 Subscript[b, 2] + 400 Subscript[b, 1] Subscript[b, 2] + 64 Subscript[b, 1]^2 Subscript[b, 2] - 64 Subscript[b, 1]^3 Subscript[b, 2] + 56 Subscript[b, 2]^2 + 64 Subscript[b, 1] Subscript[b, 2]^2 + 96 Subscript[b, 1]^2 Subscript[b, 2]^2 - 64 Subscript[b, 2]^3 - 64 Subscript[b, 1] Subscript[b, 2]^3 + 16 Subscript[b, 2]^4 + 64 Subscript[a, 1]^3 (-7 + 3 Subscript[a, 2] - 3 Subscript[b, 1] - 3 Subscript[b, 2] - 3 Subscript[b, 3]) + 16 Subscript[b, 3] + 400 Subscript[b, 1] Subscript[b, 3] + 64 Subscript[b, 1]^2 Subscript[b, 3] - 64 Subscript[b, 1]^3 Subscript[b, 3] + 400 Subscript[b, 2] Subscript[b, 3] + 640 Subscript[b, 1] Subscript[b, 2] Subscript[b, 3] + 64 Subscript[b, 1]^2 Subscript[b, 2] Subscript[b, 3] + 64 Subscript[b, 2]^2 Subscript[b, 3] + 64 Subscript[b, 1] Subscript[b, 2]^2 Subscript[b, 3] - 64 Subscript[b, 2]^3 Subscript[b, 3] + 56 Subscript[b, 3]^2 + 64 Subscript[b, 1] Subscript[b, 3]^2 + 96 Subscript[b, 1]^2 Subscript[b, 3]^2 + 64 Subscript[b, 2] Subscript[b, 3]^2 + 64 Subscript[b, 1] Subscript[b, 2] Subscript[b, 3]^2 + 96 Subscript[b, 2]^2 Subscript[b, 3]^2 - 64 Subscript[b, 3]^3 - 64 Subscript[b, 1] Subscript[b, 3]^3 - 64 Subscript[b, 2] Subscript[b, 3]^3 + 16 Subscript[b, 3]^4 - 64 Subscript[a, 2]^3 (7 + 3 Subscript[b, 1] + 3 Subscript[b, 2] + 3 Subscript[b, 3]) - 8 Subscript[a, 2]^2 (-43 + 4 Subscript[b, 1]^2 + 4 Subscript[b, 2]^2 - 72 Subscript[b, 3] + 4 Subscript[b, 3]^2 - 8 Subscript[b, 2] (9 + 5 Subscript[b, 3]) - 8 Subscript[b, 1] (9 + 5 Subscript[b, 2] + 5 Subscript[b, 3])) + 8 Subscript[a, 1]^2 (43 + 44 Subscript[a, 2]^2 - 4 Subscript[b, 1]^2 + 72 Subscript[b, 2] - 4 Subscript[b, 2]^2 + 72 Subscript[b, 3] + 40 Subscript[b, 2] Subscript[b, 3] - 4 Subscript[b, 3]^2 + 8 Subscript[b, 1] (9 + 5 Subscript[b, 2] + 5 Subscript[b, 3]) - 8 Subscript[a, 2] (9 + 5 Subscript[b, 1] + 5 Subscript[b, 2] + 5 Subscript[b, 3])) + 16 Subscript[a, 2] (-1 + 4 Subscript[b, 1]^3 + 4 Subscript[b, 2]^3 - 25 Subscript[b, 3] - 4 Subscript[b, 3]^2 + 4 Subscript[b, 3]^3 - 4 Subscript[b, 2]^2 (1 + Subscript[b, 3]) - 4 Subscript[b, 1]^2 (1 + Subscript[b, 2] + Subscript[b, 3]) - Subscript[b, 2] (25 + 40 Subscript[b, 3] + 4 Subscript[b, 3]^2) - Subscript[b, 1] (25 + 4 Subscript[b, 2]^2 + 40 Subscript[b, 3] + 4 Subscript[b, 3]^2 + 8 Subscript[b, 2] (5 + 3 Subscript[b, 3]))) + 16 Subscript[a, 1] (-1 + 12 Subscript[a, 2]^3 + 4 Subscript[b, 1]^3 - 25 Subscript[b, 2] - 4 Subscript[b, 2]^2 + 4 Subscript[b, 2]^3 - 25 Subscript[b, 3] - 40 Subscript[b, 2] Subscript[b, 3] - 4 Subscript[b, 2]^2 Subscript[b, 3] - 4 Subscript[b, 3]^2 - 4 Subscript[b, 2] Subscript[b, 3]^2 + 4 Subscript[b, 3]^3 - 4 Subscript[b, 1]^2 (1 + Subscript[b, 2] + Subscript[b, 3]) - 4 Subscript[a, 2]^2 (9 + 5 Subscript[b, 1] + 5 Subscript[b, 2] + 5 Subscript[b, 3]) - Subscript[b, 1] (25 + 4 Subscript[b, 2]^2 + 40 Subscript[b, 3] + 4 Subscript[b, 3]^2 + 8 Subscript[b, 2] (5 + 3 Subscript[b, 3])) + Subscript[a, 2] (25 + 4 Subscript[b, 1]^2 + 4 Subscript[b, 2]^2 + 40 Subscript[b, 3] + 4 Subscript[b, 3]^2 + 8 Subscript[b, 2] (5 + 3 Subscript[b, 3]) + 8 Subscript[b, 1] (5 + 3 Subscript[b, 2] + 3 Subscript[b, 3]))))

Standard Form

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MathML Form

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⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mfrac> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mo> … </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <msub> <mi> d </mi> <mn> 1 </mn> </msub> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> + </mo> <mfrac> <msub> <mi> d </mi> <mn> 2 </mn> </msub> <mi> z </mi> </mfrac> <mo> + </mo> <mo> … </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <msub> <mi> d </mi> <mn> 1 </mn> </msub> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> + </mo> <mfrac> <msub> <mi> d </mi> <mn> 2 </mn> </msub> <mi> z </mi> </mfrac> <mo> + </mo> <mo> … </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mtext> </mtext> <mo> /; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> d </mi> <mn> 1 </mn> </msub> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 16 </mn> </mfrac> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> d </mi> <mn> 2 </mn> </msub> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 512 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 144 </mn> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 1 </mn> <mn> 4 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 44 </mn> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 72 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 72 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 43 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 25 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 25 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 25 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 25 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 144 </mn> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 2 </mn> <mn> 4 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 4 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 4 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 4 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 56 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 96 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 56 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 96 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 96 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 56 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 400 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 400 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 640 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 400 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msubsup> <mi> a </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 72 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 43 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mn> 25 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 25 </mn> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ 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<times /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <pi /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <apply> <abs /> <ci> z </ci> </apply> <infinity /> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 16 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -3 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 512 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 144 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn 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<ci> b </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> 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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]