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InverseEllipticNomeQ






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseEllipticNomeQ[z] > Differentiation > Low-order differentiation





http://functions.wolfram.com/09.52.20.0005.01









  


  










Input Form





D[InverseEllipticNomeQ[z], {z, 5}] == (-(32/(Pi^10 z^5))) EllipticK[InverseEllipticNomeQ[z]]^2 (-1 + InverseEllipticNomeQ[z]) InverseEllipticNomeQ[z] (3 Pi^8 - 25 Pi^6 EllipticE[InverseEllipticNomeQ[z]] EllipticK[InverseEllipticNomeQ[z]] + 5 Pi^4 EllipticK[InverseEllipticNomeQ[z]]^2 (21 EllipticE[InverseEllipticNomeQ[z]]^2 + 5 Pi^2 InverseEllipticNomeQ[z]) - 30 Pi^2 EllipticE[InverseEllipticNomeQ[z]] EllipticK[InverseEllipticNomeQ[z]]^3 (8 EllipticE[InverseEllipticNomeQ[z]]^2 + 7 Pi^2 InverseEllipticNomeQ[z]) - 160 EllipticE[InverseEllipticNomeQ[z]] EllipticK[InverseEllipticNomeQ[z]]^7 (1 + InverseEllipticNomeQ[z]) (-2 + InverseEllipticNomeQ[z] + 2 InverseEllipticNomeQ[z]^2) - 240 EllipticE[InverseEllipticNomeQ[z]] EllipticK[InverseEllipticNomeQ[z]]^ 5 (-Pi^2 + Pi^2 InverseEllipticNomeQ[z] + 4 EllipticE[InverseEllipticNomeQ[z]]^2 InverseEllipticNomeQ[z] + 2 Pi^2 InverseEllipticNomeQ[z]^2) + 40 EllipticK[InverseEllipticNomeQ[z]]^6 (1 + InverseEllipticNomeQ[z]) (-2 Pi^2 - 12 EllipticE[InverseEllipticNomeQ[z]]^2 + Pi^2 InverseEllipticNomeQ[z] + 24 EllipticE[InverseEllipticNomeQ[z]]^2 InverseEllipticNomeQ[z] + 2 Pi^2 InverseEllipticNomeQ[z]^2) + 5 EllipticK[InverseEllipticNomeQ[z]]^4 (-7 Pi^4 + 48 EllipticE[InverseEllipticNomeQ[z]]^4 + 7 Pi^4 InverseEllipticNomeQ[z] + 144 Pi^2 EllipticE[InverseEllipticNomeQ[z]]^2 InverseEllipticNomeQ[z] + 14 Pi^4 InverseEllipticNomeQ[z]^2) + 16 EllipticK[InverseEllipticNomeQ[z]]^8 (-3 - 4 InverseEllipticNomeQ[z] + InverseEllipticNomeQ[z]^2 + 6 InverseEllipticNomeQ[z]^3 + 2 InverseEllipticNomeQ[z]^4))










Standard Form





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"z", "]"]]]], "+", RowBox[List["14", " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox[RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "2"]]]]], ")"]]]], "+", RowBox[List["16", " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "]"]], "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "-", RowBox[List["4", " ", RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]]]], "+", SuperscriptBox[RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "2"], "+", RowBox[List["6", " ", SuperscriptBox[RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "3"]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], "4"]]]]], ")"]]]]]], ")"]]]]]]]]










MathML Form







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<apply> <power /> <pi /> <cn type='integer'> 10 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <power /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> 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</apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 240 </cn> <apply> <ci> EllipticE </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> EllipticE </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 48 </cn> <apply> <power /> <apply> <ci> EllipticE </ci> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 144 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> EllipticE 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Date Added to functions.wolfram.com (modification date)





2007-05-02





© 1998- Wolfram Research, Inc.