Weierstrass zeta function: Specific values (formula 09.17.03.0008)

WeierstrassZeta

$Mathematica Notation$

Elliptic Functions

WeierstrassZeta[z,{g₂,g₃}]

Specific values

Values at fixed points

Equianharmonic case {g₂,g₃}=={0,1}

http://functions.wolfram.com/09.17.03.0008.01

Input Form

WeierstrassZeta[Subscript[\[Omega], 3], {0, 1}] == (Pi/(2 Subscript[\[Omega], 3] Sqrt[3])) E^(4 Pi (I/3))

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "3"], ",", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", RowBox[List["2", SubscriptBox["\[Omega]", "3"], SqrtBox["3"]]]], SuperscriptBox["\[ExponentialE]", RowBox[List["4", "\[Pi]", " ", RowBox[List["\[ImaginaryI]", "/", "3"]]]]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mo> ; </mo> <mn> 0 </mn> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mi> π </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mi> ⅈ </mi> <mo> / </mo> <mn> 3 </mn> </mrow> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <apply> <ci> CompoundExpression </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <times /> <pi /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <pi /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]_", "3"], ",", RowBox[List["{", RowBox[List["0", ",", "1"]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["\[Pi]", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["4", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "3"]]]], RowBox[List["2", " ", SubscriptBox["\[Omega]\[Omega]", "3"], " ", SqrtBox["3"]]]]]]]]

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

2001-10-29