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variants of this functions
EllipticThetaPrime




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticThetaPrime[4,z,q] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/09.08.20.0007.01









  


  








Input Form





D[EllipticThetaPrime[4, z, q], {z, \[Alpha]}] == 2^(\[Alpha] + 2) Sqrt[Pi] z^(1 - \[Alpha]) Sum[(-1)^(k - 1) k^2 q^k^2 HypergeometricPFQRegularized[{1}, {(3 - \[Alpha])/2, 1 - \[Alpha]/2}, (-k^2) z^2], {k, 1, Infinity}] /; Abs[q] < 1








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["EllipticThetaPrime", "[", RowBox[List["4", ",", "z_", ",", "q_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "+", "2"]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["k", "-", "1"]]], " ", SuperscriptBox["k", "2"], " ", SuperscriptBox["q", SuperscriptBox["k", "2"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "2"], ",", RowBox[List["1", "-", FractionBox["\[Alpha]", "2"]]]]], "}"]], ",", RowBox[List[RowBox[List["-", SuperscriptBox["k", "2"]]], " ", SuperscriptBox["z", "2"]]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "q", "]"]], "<", "1"]]]]]]]]


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





2001-10-29