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variants of this functions
EllipticPi




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,m] > Representations through more general functions > Through hypergeometric functions of two variables





http://functions.wolfram.com/08.03.26.0001.01









  


  








Input Form





EllipticPi[n, m] == (Pi/2) HypergeometricPFQ[{{1/2}, {1}, {1/2}}, {{1}, {}, {}}, n, m]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "m"]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "/", "2"]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", "/", "2"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "n", ",", "m"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> &#928; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <msubsup> <mi> F </mi> <mrow> <mn> 1 </mn> <mo> &#8290; </mo> <mn> 0 </mn> <mo> &#8290; </mo> <mn> 0 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> &#8290; </mo> <mn> 1 </mn> <mo> &#8290; </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mrow> <mrow> <mtable> <mtr> <mtd> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mn> 1 </mn> <mo> ; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mrow> <mn> 1 </mn> <mo> ; </mo> </mrow> <mo> ; </mo> </mrow> <mo> ; </mo> </mrow> </mtd> </mtr> </mtable> <mo> &#8290; </mo> <mi> n </mi> </mrow> <mo> , </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> EllipticPi </ci> <ci> n </ci> <ci> m </ci> </apply> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> F </ci> <apply> <times /> <cn type='integer'> 1 </cn> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <list> <list> <apply> <ci> CompoundExpression </ci> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='integer'> 1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <ci> Null </ci> </apply> </list> <list> <apply> <ci> CompoundExpression </ci> <apply> <ci> CompoundExpression </ci> <apply> <ci> CompoundExpression </ci> <cn type='integer'> 1 </cn> <ci> Null </ci> </apply> <ci> Null </ci> </apply> <ci> Null </ci> </apply> </list> </list> <ci> n </ci> </apply> <ci> m </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticPi", "[", RowBox[List["n_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "n", ",", "m"]], "]"]]]]]]]]


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





2001-10-29