Weierstrass sigma function: Series representations (formula 09.15.06.0001)

WeierstrassSigma

$Mathematica Notation$

Elliptic Functions

WeierstrassSigma[z,{g₂,g₃}]

Series representations

Generalized power series

Expansions at z==0

http://functions.wolfram.com/09.15.06.0001.01

Input Form

WeierstrassSigma[z, {Subscript[g, 2], Subscript[g, 3]}] == Sum[Subscript[d, k] z^(2 k + 1), {k, 0, Infinity}] /; Subscript[d, 0] == 1 && Subscript[d, 1] == 0 && Subscript[d, 2] == -(Subscript[g, 2]/240) && Subscript[d, 3] == -(Subscript[g, 3]/840) && Subscript[d, 4] == -(Subscript[g, 2]^2/161280) && Subscript[d, n] == Sum[\[Ellipsis] Sum[KroneckerDelta[n - Sum[j Subscript[k, j], {j, 1, n}], 0] Product[Subscript[c, j]^Subscript[k, j]/Subscript[k, j]!, {j, 1, n}], {Subscript[k, n], 0, n}], {Subscript[k, 1], 0, n}, {Subscript[k, 2], 0, n}] && Subscript[c, j] == -(Subscript[a, j]/(2 j (2 j - 1))) && Subscript[a, 1] == 0 && Subscript[a, 2] == Subscript[g, 2]/20 && Subscript[a, 3] == Subscript[g, 3]/28 && Subscript[a, k] == (3/((2 k + 1) (k - 3))) Sum[Subscript[a, l] Subscript[a, k - l], {l, 2, k - 2}]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassSigma", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SubscriptBox["d", "k"], " ", SuperscriptBox["z", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["d", "0"], "\[Equal]", "1"]], "\[And]", RowBox[List[SubscriptBox["d", "1"], "\[Equal]", "0"]], "\[And]", RowBox[List[SubscriptBox["d", "2"], "\[Equal]", RowBox[List["-", FractionBox[SubscriptBox["g", "2"], "240"]]]]], "\[And]", RowBox[List[SubscriptBox["d", "3"], "\[Equal]", RowBox[List["-", FractionBox[SubscriptBox["g", "3"], "840"]]]]], "\[And]", RowBox[List[SubscriptBox["d", "4"], "\[Equal]", RowBox[List["-", FractionBox[SubsuperscriptBox["g", "2", "2"], "161280"]]]]], "\[And]", RowBox[List[SubscriptBox["d", "n"], "\[Equal]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["k", "1"], "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["k", "2"], "=", "0"]], "n"], RowBox[List["\[Ellipsis]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["k", "n"], "=", "0"]], "n"], RowBox[List[RowBox[List["KroneckerDelta", "[", RowBox[List[RowBox[List["n", "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "n"], RowBox[List["j", " ", SubscriptBox["k", "j"]]]]]]], ",", "0"]], "]"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "n"], FractionBox[SubsuperscriptBox["c", "j", SubscriptBox["k", "j"]], RowBox[List[SubscriptBox["k", "j"], "!"]]]]]]]]]]]]]]]]], "\[And]", RowBox[List[SubscriptBox["c", "j"], "\[Equal]", RowBox[List["-", FractionBox[SubscriptBox["a", "j"], RowBox[List["2", " ", "j", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "j"]], "-", "1"]], ")"]]]]]]]]], "\[And]", " ", RowBox[List[SubscriptBox["a", "1"], "\[Equal]", "0"]], "\[And]", " ", RowBox[List[SubscriptBox["a", "2"], "\[Equal]", FractionBox[SubscriptBox["g", "2"], "20"]]], "\[And]", RowBox[List[SubscriptBox["a", "3"], "\[Equal]", FractionBox[SubscriptBox["g", "3"], "28"]]], "\[And]", RowBox[List[SubscriptBox["a", "k"], "\[Equal]", RowBox[List[FractionBox[RowBox[List["3", " "]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["k", "-", "3"]], ")"]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["l", "=", "2"]], RowBox[List["k", "-", "2"]]], RowBox[List[SubscriptBox["a", "l"], " ", SubscriptBox["a", RowBox[List["k", "-", "l"]]]]]]]]]]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mrow> <mi> σ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> 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]]]]]] </annotation> </semantics> <mo> ⩵ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <msub> <mi> d </mi> <mi> k </mi> </msub> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> d </mi> <mn> 0 </mn> </msub> <mo> ⩵ </mo> <mn> 1 </mn> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> d </mi> <mn> 1 </mn> </msub> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> d </mi> <mn> 2 </mn> </msub> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mn> 240 </mn> </mfrac> </mrow> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> d </mi> <mn> 3 </mn> </msub> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mn> 840 </mn> </mfrac> </mrow> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> d </mi> <mn> 4 </mn> </msub> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <msubsup> <mi> g </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mn> 161280 </mn> </mfrac> </mrow> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> d </mi> <mi> n </mi> </msub> <mo> ⩵ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <msub> <mi> k </mi> <mn> 1 </mn> </msub> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <munderover> <mo> ∑ </mo> <mrow> <msub> <mi> k </mi> <mn> 2 </mn> </msub> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mo> … </mo> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <msub> <mi> k </mi> <mi> n </mi> </msub> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <msub> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mrow> <mrow> <mi> n </mi> <mo> - </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mi> j </mi> <mo> ⁢ </mo> <msub> <mi> k </mi> <mi> j </mi> </msub> </mrow> </mrow> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> </msub> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mfrac> <msubsup> <mi> c </mi> <mi> j </mi> <msub> <mi> k </mi> <mi> j </mi> </msub> </msubsup> <mrow> <msub> <mi> k </mi> <mi> j </mi> </msub> <mo> ! </mo> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> c </mi> <mi> j </mi> </msub> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <msub> <mi> a </mi> <mi> j </mi> </msub> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> j </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> ⩵ </mo> <mfrac> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mn> 20 </mn> </mfrac> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> ⩵ </mo> <mfrac> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mn> 28 </mn> </mfrac> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 3 </mn> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> l </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </munderover> <mrow> <msub> <mi> a </mi> <mi> l </mi> </msub> <mo> ⁢ </mo> <msub> <mi> a </mi> <mrow> <mi> k </mi> <mo> - </mo> <mi> l </mi> </mrow> </msub> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> WeierstrassSigma </ci> <ci> z </ci> <list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ci> Subscript </ci> <ci> d </ci> <ci> k </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 240 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 840 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 161280 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> d </ci> <ci> n </ci> </apply> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <ci> … </ci> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> k </ci> <ci> n </ci> </apply> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <ci> KroneckerDelta </ci> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <ci> j </ci> <apply> <ci> Subscript </ci> <ci> k </ci> <ci> j </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <product /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> j </ci> </apply> <apply> <ci> Subscript </ci> <ci> k </ci> <ci> j </ci> </apply> </apply> <apply> <power /> <apply> <factorial /> <apply> <ci> Subscript </ci> <ci> k </ci> <ci> j </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> j </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> j </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 20 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 28 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> k </ci> <cn type='integer'> -3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> l </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> k </ci> <cn type='integer'> -2 </cn> </apply> </uplimit> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> l </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> l </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassSigma", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[SubscriptBox["d", "k"], " ", SuperscriptBox["z", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["d", "0"], "\[Equal]", "1"]], "&&", RowBox[List[SubscriptBox["d", "1"], "\[Equal]", "0"]], "&&", RowBox[List[SubscriptBox["d", "2"], "\[Equal]", RowBox[List["-", FractionBox[SubscriptBox["g", "2"], "240"]]]]], "&&", RowBox[List[SubscriptBox["d", "3"], "\[Equal]", RowBox[List["-", FractionBox[SubscriptBox["g", "3"], "840"]]]]], "&&", RowBox[List[SubscriptBox["d", "4"], "\[Equal]", RowBox[List["-", FractionBox[SubsuperscriptBox["g", "2", "2"], "161280"]]]]], "&&", RowBox[List[SubscriptBox["d", "n"], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["k", "1"], "=", "0"]], "n"], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["k", "2"], "=", "0"]], "n"], RowBox[List["\[Ellipsis]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List[SubscriptBox["k", "n"], "=", "0"]], "n"], RowBox[List[RowBox[List["KroneckerDelta", "[", RowBox[List[RowBox[List["n", "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "n"], RowBox[List["j", " ", SubscriptBox["k", "j"]]]]]]], ",", "0"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], "n"], FractionBox[SubsuperscriptBox["c", "j", SubscriptBox["k", "j"]], RowBox[List[SubscriptBox["k", "j"], "!"]]]]]]]]]]]]]]]]], "&&", RowBox[List[SubscriptBox["c", "j"], "\[Equal]", RowBox[List["-", FractionBox[SubscriptBox["a", "j"], RowBox[List["2", " ", "j", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "j"]], "-", "1"]], ")"]]]]]]]]], "&&", RowBox[List[SubscriptBox["a", "1"], "\[Equal]", "0"]], "&&", RowBox[List[SubscriptBox["a", "2"], "\[Equal]", FractionBox[SubscriptBox["g", "2"], "20"]]], "&&", RowBox[List[SubscriptBox["a", "3"], "\[Equal]", FractionBox[SubscriptBox["g", "3"], "28"]]], "&&", RowBox[List[SubscriptBox["a", "k"], "\[Equal]", FractionBox[RowBox[List["3", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["l", "=", "2"]], RowBox[List["k", "-", "2"]]], RowBox[List[SubscriptBox["a", "l"], " ", SubscriptBox["a", RowBox[List["k", "-", "l"]]]]]]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["k", "-", "3"]], ")"]]]]]]]]]]]]]]]

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

2001-10-29

WeierstrassSigma[n,z,{g₂,g₃}]