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WeierstrassZeta




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassZeta[z,{g2,g3}] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/09.17.20.0010.01









  


  








Input Form





D[WeierstrassZeta[z, {Subscript[g, 2], Subscript[g, 3]}], {z, \[Alpha]}] == FDPowerConstant[z, -1, \[Alpha]] z^(-\[Alpha] - 1) - 2 z^(2 - \[Alpha]) Sum[If[{m, n} == {0, 0}, 0, (1/(2 m Subscript[\[Omega], 1] + 2 n Subscript[\[Omega], 3])^3) Hypergeometric2F1Regularized[1, 3, 3 - \[Alpha], z/(2 m Subscript[\[Omega], 1] + 2 n Subscript[\[Omega], 3])]], {m, -Infinity, Infinity}, {n, -Infinity, 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["WeierstrassZeta", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["FDPowerConstant", "[", RowBox[List["z", ",", RowBox[List["-", "1"]], ",", "\[Alpha]"]], "]"]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "\[Alpha]"]], "-", "1"]]]]], "-", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["2", "-", "\[Alpha]"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["n", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["If", "[", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["m", ",", "n"]], "}"]], "\[Equal]", RowBox[List["{", RowBox[List["0", ",", "0"]], "}"]]]], ",", "0", ",", FractionBox[RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["1", ",", "3", ",", RowBox[List["3", "-", "\[Alpha]"]], ",", FractionBox["z", RowBox[List[RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]]]]]]], "]"]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]]]], ")"]], "3"]]]], "]"]]]]]]]]]]]]]]


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





2001-10-29