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http://functions.wolfram.com/08.06.03.0001.01
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EllipticPi[n, z, 0] == ArcTanh[Sqrt[n - 1] Tan[z]]/Sqrt[n - 1]
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Cell[BoxData[RowBox[List[RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "z", ",", "0"]], "]"]], "\[Equal]", FractionBox[RowBox[List["ArcTanh", "[", RowBox[List[SqrtBox[RowBox[List["n", "-", "1"]]], " ", RowBox[List["Tan", "[", "z", "]"]]]], "]"]], SqrtBox[RowBox[List["n", "-", "1"]]]]]]]]
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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> <mi> z </mi> <mo> ❘ </mo> <mn> 0 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <msqrt> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <msqrt> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> EllipticPi </ci> <ci> n </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <apply> <arctanh /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <tan /> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticPi", "[", RowBox[List["n_", ",", "z_", ",", "0"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["ArcTanh", "[", RowBox[List[SqrtBox[RowBox[List["n", "-", "1"]]], " ", RowBox[List["Tan", "[", "z", "]"]]]], "]"]], SqrtBox[RowBox[List["n", "-", "1"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
