Jacobi zeta function: General characteristics (formula 08.07.04.0010)

JacobiZeta

$Mathematica Notation$

Elliptic Integrals

JacobiZeta[z,m]

General characteristics

Symmetries and periodicities

Periodicity

http://functions.wolfram.com/08.07.04.0010.01

Input Form

JacobiZeta[z + Pi, m] == JacobiZeta[z, m]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["z", "+", "\[Pi]"]], ",", "m"]], "]"]], "\[Equal]", RowBox[List["JacobiZeta", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]

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> <mi> z </mi> <mo> + </mo> <mi> π </mi> </mrow> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> Ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiZeta </ci> <apply> <plus /> <ci> z </ci> <pi /> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiZeta </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["z_", "+", "\[Pi]"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["JacobiZeta", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]

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

2007-05-02