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JacobiSD




Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiSD[z,m] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/09.35.20.0006.01









  


  








Input Form





D[JacobiSD[z, m], {z, \[Alpha]}] == ((2^(\[Alpha] - 1) Pi^(5/2) z^(1 - \[Alpha]))/(Sqrt[1 - m] Sqrt[m] EllipticK[m]^2)) Sum[(((-1)^k (2 k + 1) EllipticNomeQ[m]^(k + 1/2))/ (EllipticNomeQ[m]^(2 k + 1) + 1)) HypergeometricPFQRegularized[{1}, {1 - \[Alpha]/2, (3 - \[Alpha])/2}, -(((2 k + 1)^2 Pi^2 z^2)/(16 EllipticK[m]^2))], {k, 0, Infinity}]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["JacobiSD", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "-", "1"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["5", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticNomeQ", "[", "m", "]"]], RowBox[List["k", "+", FractionBox["1", "2"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["\[Alpha]", "2"]]], ",", FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "2"]]], "}"]], ",", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], "2"], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]], RowBox[List["16", " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "2"]]]]]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["EllipticNomeQ", "[", "m", "]"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], "+", "1"]]]]]]], RowBox[List[SqrtBox[RowBox[List["1", "-", "m"]]], " ", SqrtBox["m"], " ", SuperscriptBox[RowBox[List["EllipticK", "[", "m", "]"]], "2"]]]]]]]]


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





2001-10-29