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 WeierstrassSigma

 http://functions.wolfram.com/09.16.06.0004.01

 Input Form

 WeierstrassSigma[i, z, {Subscript[g, 2], Subscript[g, 3]}] == z Exp[-Sum[(z^(2 j)/(2 j)) Sum[If[{m, n} == {0, 0}, 0, 1/(2 m Subscript[\[Omega], 1] + 2 n Subscript[\[Omega], 3])^(2 j)], {m, -Infinity, Infinity}, {n, -Infinity, Infinity}], {j, 2, Infinity}]] (-Subscript[e, i] + 1/z^2 + Sum[(2 j + 1) z^(2 j) Sum[If[{m, n} == {0, 0}, 0, (2 m Subscript[\[Omega], 1] + 2 n Subscript[\[Omega], 3])^ (-(2 j + 2))], {m, -Infinity, Infinity}, {n, -Infinity, Infinity}], {j, 1, Infinity}])^(1/2) /; Element[i, {1, 2, 3}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List["i", ",", "z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List["z", " ", RowBox[List["Exp", "[", RowBox[List["-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "2"]], "\[Infinity]"], RowBox[List[FractionBox[SuperscriptBox["z", RowBox[List["2", "j"]]], RowBox[List["2", "j"]]], RowBox[List["(", 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["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", "n", " ", SubscriptBox["\[Omega]", "3"]]]]], ")"]], RowBox[List["2", "j"]]]]]], "]"]]]]]], ")"]]]]]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["e", "i"]]], "+", FractionBox["1", SuperscriptBox["z", "2"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "j"]], "+", "1"]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", "j"]]], " ", RowBox[List["(", " ", 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", ",", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", "n", " ", SubscriptBox["\[Omega]", "3"]]]]], ")"]], RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["2", "j"]], "+", "2"]], ")"]]]]]]], "]"]]]]]], ")"]]]]]]]], ")"]], RowBox[List["1", "/", "2"]]]]]]], "/;", RowBox[List["i", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]

 MathML Form

 σ i ( z TagBox["z", Rule[Editable, True]] ; g 2 TagBox[SubscriptBox["g", "2"], Rule[Editable, True]] , g 3 TagBox[SubscriptBox["g", "3"], Rule[Editable, True]] ) z exp ( - j = 2 z 2 j 2 j m , n = - { m , n } { 0 , 0 } 1 ( 2 m ω 1 + 2 n ω 3 ) 2 j ) ( - e i + 1 z 2 + j = 1 ( 2 j + 1 ) z 2 j m , n = - { m , n } { 0 , 0 } 1 ( 2 m ω 1 + 2 n ω 3 ) 2 j + 2 ) 1 / 2 /; i { 1 , 2 , 3 } FormBox RowBox RowBox RowBox SubscriptBox σ i ( RowBox RowBox TagBox z Rule Editable ; TagBox SubscriptBox g 2 Rule Editable , TagBox SubscriptBox g 3 Rule Editable ) RowBox z RowBox Exp [ RowBox - RowBox UnderoverscriptBox RowBox j = 2 ErrorBox RowBox FractionBox SuperscriptBox z RowBox 2 j RowBox 2 j RowBox UnderoverscriptBox UnderscriptBox RowBox m , RowBox n = RowBox - RowBox RowBox { RowBox m , n } RowBox { RowBox 0 , 0 } FractionBox 1 SuperscriptBox RowBox ( RowBox RowBox 2 m SubscriptBox ω 1 + RowBox 2 n SubscriptBox ω 3 ) RowBox 2 j ] SuperscriptBox RowBox ( RowBox RowBox - SubscriptBox e i + FractionBox 1 SuperscriptBox z 2 + RowBox UnderoverscriptBox RowBox j = 1 RowBox RowBox ( RowBox RowBox 2 j + 1 ) SuperscriptBox z RowBox 2 j RowBox UnderoverscriptBox UnderscriptBox RowBox m , RowBox n = RowBox - RowBox RowBox { RowBox m , n } RowBox { RowBox 0 , 0 } FractionBox 1 SuperscriptBox RowBox ( RowBox RowBox 2 m SubscriptBox ω 1 + RowBox 2 n SubscriptBox ω 3 ) RowBox RowBox 2 j + 2 ) RowBox 1 / 2 /; RowBox i RowBox { RowBox 1 , 2 , 3 } TraditionalForm [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List["i_", ",", "z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["z", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "2"]], "\[Infinity]"], FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["2", " ", "j"]]], " ", 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["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]]]], ")"]], RowBox[List["2", " ", "j"]]]]]], "]"]]]]]]]], RowBox[List["2", " ", "j"]]]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["-", SubscriptBox["e", "i"]]], "+", FractionBox["1", SuperscriptBox["z", "2"]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", " ", "j"]]], " ", 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", ",", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m", " ", SubscriptBox["\[Omega]", "1"]]], "+", RowBox[List["2", " ", "n", " ", SubscriptBox["\[Omega]", "3"]]]]], ")"]], RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "j"]], "+", "2"]], ")"]]]]]]], "]"]]]]]]]]]]]]]]], "/;", RowBox[List["i", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]]]

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

 2001-10-29