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http://functions.wolfram.com/08.06.06.0008.01
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EllipticPi[n, z, m] \[Proportional] EllipticPi[Subscript[n, 0], z, m] +
(1/(2 (m - Subscript[n, 0]) (-1 + Subscript[n, 0])))
(EllipticE[z, m] + (-1 + m/Subscript[n, 0]) EllipticF[z, m] -
((m - Subscript[n, 0]^2)/Subscript[n, 0]) EllipticPi[Subscript[n, 0], z,
m] + (Subscript[n, 0] Sqrt[1 - m Sin[z]^2] Sin[2 z])/
(2 (Subscript[n, 0] Sin[z]^2 - 1))) (n - Subscript[n, 0]) +
(1/(4 (m - Subscript[n, 0])^2 (Subscript[n, 0] - 1)^2))
((Sin[2 z]/(8 (-1 + Subscript[n, 0] Sin[z]^2)^2)) Sqrt[1 - m Sin[z]^2]
(6 m - m Subscript[n, 0] - 2 (4 + m) Subscript[n, 0]^2 +
5 Subscript[n, 0]^3 + Subscript[n, 0] (m + 2 m Subscript[n, 0] +
(2 - 5 Subscript[n, 0]) Subscript[n, 0]) Cos[2 z]) +
(1/(2 Subscript[n, 0]^2)) ((-Subscript[n, 0]) (m + 2 m Subscript[n, 0] +
(2 - 5 Subscript[n, 0]) Subscript[n, 0]) EllipticE[z, m] +
(m^2 (1 - 4 Subscript[n, 0]) + (2 - 5 Subscript[n, 0])
Subscript[n, 0]^2 + 3 m Subscript[n, 0] (-1 + 3 Subscript[n, 0]))
EllipticF[z, m] + (2 m (2 - 5 Subscript[n, 0]) Subscript[n, 0] +
3 Subscript[n, 0]^4 + m^2 (-1 + 4 Subscript[n, 0]))
EllipticPi[Subscript[n, 0], z, m])) (n - Subscript[n, 0])^2 +
\[Ellipsis] /; (n -> Subscript[n, 0])
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Cell[BoxData[RowBox[List[RowBox[List[StyleBox[RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "z", ",", "m"]], "]"]], Rule[FormatType, StandardForm]], "\[Proportional]", RowBox[List[StyleBox[RowBox[List["EllipticPi", "[", RowBox[List[SubscriptBox["n", "0"], ",", "z", ",", "m"]], "]"]], Rule[FormatType, StandardForm]], StyleBox["+", Rule[FormatType, StandardForm]], RowBox[List[FractionBox["1", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m", "-", SubscriptBox["n", "0"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["n", "0"]]], ")"]]]]], RowBox[List["(", RowBox[List[RowBox[List["EllipticE", "[", RowBox[List["z", ",", "m"]], "]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", FractionBox["m", SubscriptBox["n", "0"]]]], ")"]], " ", RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["m", "-", SubsuperscriptBox["n", "0", "2"]]], SubscriptBox["n", "0"]], RowBox[List["EllipticPi", "[", RowBox[List[SubscriptBox["n", "0"], ",", "z", ",", "m"]], "]"]]]], " ", "+", FractionBox[RowBox[List[" ", RowBox[List[SubscriptBox["n", "0"], SqrtBox[RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]]], " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]]]]]], RowBox[List["2", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["n", "0"], SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]], " ", "-", "1"]], ")"]]]]]]], ")"]], RowBox[List["(", RowBox[List["n", "-", SubscriptBox["n", "0"]]], ")"]]]], " ", "+", RowBox[List[FractionBox["1", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["m", "-", SubscriptBox["n", "0"]]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["n", "0"], "-", "1"]], ")"]], "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List["2", " ", "z"]], "]"]], RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[SubscriptBox["n", "0"], " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]], ")"]], "2"]]]], SqrtBox[RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox[RowBox[List["Sin", "[", "z", "]"]], "2"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", "m"]], "-", RowBox[List["m", " ", SubscriptBox["n", "0"]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["4", "+", "m"]], ")"]], " ", SubsuperscriptBox["n", "0", "2"]]], "+", RowBox[List["5", " ", SubsuperscriptBox["n", "0", "3"]]], "+", RowBox[List[SubscriptBox["n", "0"], " ", RowBox[List["(", RowBox[List["m", "+", RowBox[List["2", " ", "m", " ", SubscriptBox["n", "0"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "-", RowBox[List["5", " ", SubscriptBox["n", "0"]]]]], ")"]], " ", SubscriptBox["n", "0"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["2", " ", SubsuperscriptBox["n", "0", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["n", "0"]]], " ", RowBox[List["(", RowBox[List["m", "+", RowBox[List["2", " ", "m", " ", SubscriptBox["n", "0"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "-", RowBox[List["5", " ", SubscriptBox["n", "0"]]]]], ")"]], " ", SubscriptBox["n", "0"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List["z", ",", "m"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["m", "2"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", SubscriptBox["n", "0"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "-", RowBox[List["5", " ", SubscriptBox["n", "0"]]]]], ")"]], " ", SubsuperscriptBox["n", "0", "2"]]], "+", RowBox[List["3", " ", "m", " ", SubscriptBox["n", "0"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["3", " ", SubscriptBox["n", "0"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticF", "[", RowBox[List["z", ",", "m"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m", " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["5", " ", SubscriptBox["n", "0"]]]]], ")"]], " ", SubscriptBox["n", "0"]]], "+", RowBox[List["3", " ", SubsuperscriptBox["n", "0", "4"]]], "+", RowBox[List[SuperscriptBox["m", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", SubscriptBox["n", "0"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticPi", "[", RowBox[List[SubscriptBox["n", "0"], ",", "z", ",", "m"]], "]"]]]]]], ")"]]]]]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["n", "-", SubscriptBox["n", "0"]]], ")"]], "2"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["n", "\[Rule]", SubscriptBox["n", "0"]]], ")"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> Π </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> ; </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mi> Π </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> ; </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <msubsup> <mi> n </mi> <mn> 0 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Π </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> ; </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mfrac> <mo> + </mo> <mrow> <mrow> <mi> F </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mi> m </mi> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mfrac> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msubsup> <mi> n </mi> <mn> 0 </mn> <mn> 2 </mn> </msubsup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> m </mi> <mo> + </mo> <mrow> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> F </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <msubsup> <mi> n </mi> <mn> 0 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> Π </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> ; </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msubsup> <mi> n </mi> <mn> 0 </mn> <mn> 4 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> m </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msubsup> <mi> n </mi> <mn> 0 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msubsup> <mi> n </mi> <mn> 0 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> ⁢ </mo> <mi> m </mi> </mrow> <mo> + </mo> <mi> m </mi> <mo> + </mo> <mrow> <msub> <mi> n </mi> <mn> 0 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <msub> <mi> n </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> EllipticPi </ci> <ci> n </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <ci> EllipticPi </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> EllipticE </ci> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> EllipticPi </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> <ci> z </ci> <ci> m </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> EllipticF </ci> <ci> z 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<cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <ci> m </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> m </ci> <apply> <power /> <apply> <sin /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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