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http://functions.wolfram.com/08.06.03.0006.01
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EllipticPi[n, ArcCsc[Sqrt[m]], m] == (1/Sqrt[m]) EllipticPi[n/m, 1/m]
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Cell[BoxData[RowBox[List[RowBox[List["EllipticPi", "[", RowBox[List["n", ",", RowBox[List["ArcCsc", "[", SqrtBox["m"], "]"]], ",", "m"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox["m"]], RowBox[List["EllipticPi", "[", RowBox[List[FractionBox["n", "m"], ",", FractionBox["1", "m"]]], "]"]]]]]]]]
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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> <mi> Π </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> ; </mo> <mrow> <mrow> <msup> <mi> csc </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> m </mi> </msqrt> <mo> ) </mo> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mi> m </mi> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mi> Π </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mi> n </mi> <mi> m </mi> </mfrac> <mo> ❘ </mo> <mfrac> <mn> 1 </mn> <mi> m </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> EllipticPi </ci> <ci> n </ci> <apply> <arccsc /> <apply> <power /> <ci> m </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> m </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> m </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> EllipticPi </ci> <apply> <times /> <ci> n </ci> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticPi", "[", RowBox[List["n_", ",", RowBox[List["ArcCsc", "[", SqrtBox["m_"], "]"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["EllipticPi", "[", RowBox[List[FractionBox["n", "m"], ",", FractionBox["1", "m"]]], "]"]], SqrtBox["m"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
