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EllipticNomeQ




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticNomeQ[m] > Differentiation > Low-order differentiation





http://functions.wolfram.com/09.53.20.0006.01









  


  








Input Form





D[EllipticNomeQ[m], {m, 5}] == -(Pi^2 (Pi^8 + 8 EllipticK[m] (5 m Pi^6 EllipticK[m] + 10 (1 + m (-1 + 7 m)) Pi^4 EllipticK[m]^3 + 240 EllipticE[m]^4 EllipticK[m]^3 + 20 (-1 + 5 m) (2 + m (-1 + 4 m)) Pi^2 EllipticK[m]^5 + 32 (4 + m (-18 + m (37 + m (-23 + 24 m)))) EllipticK[m]^7 - 240 EllipticE[m]^3 EllipticK[m]^2 (Pi^2 + 4 m EllipticK[m]^2) + 60 EllipticE[m]^2 EllipticK[m] (Pi^4 + 12 m Pi^2 EllipticK[m]^2 + 4 (1 + m (-1 + 7 m)) EllipticK[m]^4) + 5 EllipticE[m] (-Pi^6 - 24 m Pi^4 EllipticK[m]^2 - 24 (1 + m (-1 + 7 m)) Pi^2 EllipticK[m]^4 - 16 (-1 + 5 m) (2 + m (-1 + 4 m)) EllipticK[m]^6))) EllipticNomeQ[m])/(1024 (-1 + m)^5 m^5 EllipticK[m]^10)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["m", ",", "5"]], "}"]]], RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "8"], "+", RowBox[List["8", " ", RowBox[List["EllipticK", "[", "m", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", "m", " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[List["EllipticK", "[", "m", "]"]]]], "+", RowBox[List["10", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["7", " ", "m"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "3"]]], "+", RowBox[List["240", " ", SuperscriptBox[RowBox[List["EllipticE", "[", "m", "]"]], "4"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "3"]]], "+", RowBox[List["20", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["5", " ", "m"]]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", "m"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "5"]]], "+", RowBox[List["32", " ", RowBox[List["(", RowBox[List["4", "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "18"]], "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List["37", "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "23"]], "+", RowBox[List["24", " ", "m"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "7"]]], "-", RowBox[List["240", " ", SuperscriptBox[RowBox[List["EllipticE", "[", "m", "]"]], "3"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], "+", RowBox[List["4", " ", "m", " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "2"]]]]], ")"]]]], "+", RowBox[List["60", " ", SuperscriptBox[RowBox[List["EllipticE", "[", "m", "]"]], "2"], " ", RowBox[List["EllipticK", "[", "m", "]"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "4"], "+", RowBox[List["12", " ", "m", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "2"]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["7", " ", "m"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "4"]]]]], ")"]]]], "+", RowBox[List["5", " ", RowBox[List["EllipticE", "[", "m", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["\[Pi]", "6"]]], "-", RowBox[List["24", " ", "m", " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "2"]]], "-", RowBox[List["24", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["7", " ", "m"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "4"]]], "-", RowBox[List["16", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["5", " ", "m"]]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", "m"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "6"]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticNomeQ", "[", "m", "]"]]]], ")"]]]], "/", RowBox[List["(", RowBox[List["1024", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], "5"], " ", SuperscriptBox["m", "5"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "10"]]], ")"]]]]]]]]








MathML Form







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<power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 240 </cn> <apply> <power /> <apply> <ci> EllipticE </ci> <ci> m </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 240 </cn> <apply> <power /> <apply> <ci> EllipticE </ci> <ci> m </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> m </ci> <apply> <power /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <ci> m </ci> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <power /> <apply> <ci> EllipticE </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <ci> m </ci> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <ci> EllipticE </ci> <ci> m </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -16 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <plus /> <apply> <times /> <ci> m </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> m </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 24 </cn> <ci> m </ci> <apply> <power /> <pi /> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <pi /> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <ci> EllipticNomeQ </ci> <ci> m </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02