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variants of this functions
EllipticPi




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticPi[n,m] > Differentiation > Low-order differentiation > With respect to m





http://functions.wolfram.com/08.03.20.0003.01









  


  








Input Form





D[EllipticPi[n, m], m] == (1/(2 (n - m))) (EllipticE[m]/(m - 1) + EllipticPi[n, m])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "m"], RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "m"]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", RowBox[List["(", RowBox[List["n", "-", "m"]], ")"]]]]], RowBox[List["(", RowBox[List[FractionBox[RowBox[List["EllipticE", "[", "m", "]"]], RowBox[List["m", "-", "1"]]], "+", RowBox[List["EllipticPi", "[", 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> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mi> &#928; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> + </mo> <mrow> <mi> &#928; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> m </ci> </bvar> <apply> <ci> EllipticPi </ci> <ci> n </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> EllipticE </ci> <ci> m </ci> </apply> <apply> <power /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> EllipticPi </ci> <ci> n </ci> <ci> m </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["m_"]]], RowBox[List["EllipticPi", "[", RowBox[List["n_", ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[FractionBox[RowBox[List["EllipticE", "[", "m", "]"]], RowBox[List["m", "-", "1"]]], "+", RowBox[List["EllipticPi", "[", RowBox[List["n", ",", "m"]], "]"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["n", "-", "m"]], ")"]]]]]]]]]


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





2001-10-29