D[EllipticE[z], z] == (EllipticE[z] - EllipticK[z])/(2 z)

Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["EllipticE", "[", "z", "]"]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["EllipticE", "[", "z", "]"]], "-", RowBox[List["EllipticK", "[", "z", "]"]]]], RowBox[List["2", " ", "z"]]]]]]]

<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> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> EllipticE </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> EllipticE </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> EllipticK </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["EllipticE", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["EllipticE", "[", "z", "]"]], "-", RowBox[List["EllipticK", "[", "z", "]"]]]], RowBox[List["2", " ", "z"]]]]]]]

2001-10-29