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 WeierstrassSigma

 http://functions.wolfram.com/09.15.20.0012.01

 Input Form

 D[WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}], {z, \[Alpha]}] == 2^(\[Alpha] - 1) Sqrt[Pi] z^(1 - \[Alpha]) Product[1/(1 - q^(2 n)), {n, 1, Infinity}]^3 Sum[(-1)^(j + k) q^(k (1 + k)) (2 k + 1)^(2 j + 1) ((Pi z)/(4 Subscript[\[Omega], 1]))^(2 j) HypergeometricPFQRegularized[ {1 + j, 3/2 + j}, {1 + j - \[Alpha]/2, (3 - \[Alpha])/2 + j}, (z^2/(2 Subscript[\[Omega], 1])) WeierstrassZeta[Subscript[\[Omega], 1], {Subscript[g, 2], Subscript[g, 3]}]], {k, 0, Infinity}, {j, 0, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "\[Alpha]"]], "}"]]], RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "-", "1"]]], SqrtBox["\[Pi]"], SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]], SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["n", "=", "1"]], "\[Infinity]"], FractionBox["1", RowBox[List["1", "-", SuperscriptBox["q", RowBox[List["2", "n"]]]]]]]], ")"]], "3"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["j", "+", "k"]]], " ", SuperscriptBox["q", RowBox[List["k", " ", RowBox[List["(", RowBox[List["1", "+", "k"]], ")"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]], SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["4", SubscriptBox["\[Omega]", "1"]]]], ")"]], RowBox[List["2", " ", "j"]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", "j"]], ",", RowBox[List[FractionBox["3", "2"], "+", "j"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", "j", "-", FractionBox["\[Alpha]", "2"]]], ",", RowBox[List[FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "2"], "+", "j"]]]], "}"]], ",", RowBox[List[FractionBox[SuperscriptBox["z", "2"], RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]], RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]], "]"]]]]]]]]]]]]]]

 MathML Form

 α σ ( z ; g 2 , g 3 ) TagBox[RowBox[List["\[Sigma]", "(", RowBox[List[RowBox[List[TagBox["z", Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassSigma[Slot[1], List[Slot[2], Slot[3]]]]]] z α 2 α - 1 π z 1 - α ( n = 1 1 1 - q 2 n ) 3 k = 0 j = 0 ( - 1 ) j + k q k ( k + 1 ) ( 2 k + 1 ) 2 j + 1 ( π z 4 ω 1 ) 2 j 2 F ~ 2 ( j + 1 , j + 3 2 ; j - α 2 + 1 , j + 3 - α 2 ; z 2 ζ ( ω 1 ; g 2 , g 3 ) 2 ω 1 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["j", "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["j", "+", FractionBox["3", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["j", "-", FractionBox["\[Alpha]", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["j", "+", FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[FractionBox[RowBox[List[SuperscriptBox["z", "2"], " ", TagBox[RowBox[List["\[Zeta]", "(", RowBox[List[RowBox[List[TagBox[SubscriptBox["\[Omega]", "1"], Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]]]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] z α WeierstrassSigma z Subscript g 2 Subscript g 3 2 α -1 1 2 z 1 -1 α n 1 1 1 -1 q 2 n -1 3 j 0 k 0 -1 j k q k k 1 2 k 1 2 j 1 z 4 Subscript ω 1 -1 2 j HypergeometricPFQRegularized j 1 j 3 2 j -1 α 2 -1 1 j 3 -1 α 2 -1 z 2 WeierstrassZeta Subscript ω 1 Subscript g 2 Subscript g 3 2 Subscript ω 1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["WeierstrassSigma", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["2", RowBox[List["\[Alpha]", "-", "1"]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["n", "=", "1"]], "\[Infinity]"], FractionBox["1", RowBox[List["1", "-", SuperscriptBox["q", RowBox[List["2", " ", "n"]]]]]]]], ")"]], "3"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], "\[Infinity]"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["j", "+", "k"]]], " ", SuperscriptBox["q", RowBox[List["k", " ", RowBox[List["(", RowBox[List["1", "+", "k"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[Pi]", " ", "z"]], RowBox[List["4", " ", SubscriptBox["\[Omega]", "1"]]]], ")"]], RowBox[List["2", " ", "j"]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", "j"]], ",", RowBox[List[FractionBox["3", "2"], "+", "j"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", "j", "-", FractionBox["\[Alpha]", "2"]]], ",", RowBox[List[FractionBox[RowBox[List["3", "-", "\[Alpha]"]], "2"], "+", "j"]]]], "}"]], ",", FractionBox[RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], RowBox[List["2", " ", SubscriptBox["\[Omega]", "1"]]]]]], "]"]]]]]]]]]]]]]]

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

 2001-10-29