Inverse elliptic nome: Differentiation (formula 09.52.20.0004)

InverseEllipticNomeQ

$Mathematica Notation$

Elliptic Functions

InverseEllipticNomeQ[z]

Differentiation

Low-order differentiation

http://functions.wolfram.com/09.52.20.0004.01

Input Form

D[InverseEllipticNomeQ[z], {z, 4}] == (8/(Pi^8 z^4)) EllipticK[InverseEllipticNomeQ[z]]^2 (-1 + InverseEllipticNomeQ[z]) InverseEllipticNomeQ[z] (3 Pi^6 - 22 Pi^4 EllipticE[InverseEllipticNomeQ[z]] EllipticK[InverseEllipticNomeQ[z]] - 96 EllipticE[InverseEllipticNomeQ[z]] EllipticK[InverseEllipticNomeQ[z]]^5 (1 + InverseEllipticNomeQ[z]) (-1 + 2 InverseEllipticNomeQ[z]) - 48 EllipticE[InverseEllipticNomeQ[z]] EllipticK[InverseEllipticNomeQ[z]]^3 (2 EllipticE[InverseEllipticNomeQ[z]]^2 + 3 Pi^2 InverseEllipticNomeQ[z]) + 2 Pi^2 EllipticK[InverseEllipticNomeQ[z]]^2 (36 EllipticE[InverseEllipticNomeQ[z]]^2 + 11 Pi^2 InverseEllipticNomeQ[z]) + 16 EllipticK[InverseEllipticNomeQ[z]]^6 (1 + InverseEllipticNomeQ[z]) (-2 + InverseEllipticNomeQ[z] + 2 InverseEllipticNomeQ[z]^2) + 24 EllipticK[InverseEllipticNomeQ[z]]^4 (-Pi^2 + Pi^2 InverseEllipticNomeQ[z] + 12 EllipticE[InverseEllipticNomeQ[z]]^2 InverseEllipticNomeQ[z] + 2 Pi^2 InverseEllipticNomeQ[z]^2))

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "4"]], "}"]]], RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]]]], "\[Equal]", RowBox[List[FractionBox["8", RowBox[List[SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["z", "4"]]]], SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]]]], ")"]], " ", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["\[Pi]", "6"]]], "-", RowBox[List["22", " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[List["EllipticE", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], " ", RowBox[List["EllipticK", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]]]], "-", RowBox[List["96", " ", RowBox[List["EllipticE", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], "5"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]]]]]], ")"]]]], "-", RowBox[List["48", " ", RowBox[List["EllipticE", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], "2"]]], "+", RowBox[List["3", " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["36", " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], "2"]]], "+", RowBox[List["11", " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]]]]]], ")"]]]], "+", RowBox[List["16", " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], "6"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "2"]]]]], ")"]]]], "+", RowBox[List["24", " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["\[Pi]", "2"]]], "+", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]]]], "+", RowBox[List["12", " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], "2"], " ", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "2"]]]]], ")"]]]]]], ")"]]]]]]]]

MathML Form

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<annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <mrow> <msup> <mi> π </mi> <mn> 8 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 96 </mn> <mo> ⁢ </mo> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 48 </mn> <mo> ⁢ </mo> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 36 </mn> <mo> ⁢ </mo> <msup> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 22 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 6 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 4 </cn> </degree> </bvar> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='integer'> -2 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 96 </cn> <apply> <ci> EllipticE </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> EllipticE </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 48 </cn> <apply> <ci> EllipticE </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> EllipticE </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <power /> <apply> <ci> EllipticE </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 22 </cn> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <apply> <ci> EllipticK </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2007-05-02