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JacobiZeta




Mathematica Notation

Traditional Notation









Elliptic Integrals > JacobiZeta[z,m] > General characteristics > Symmetries and periodicities > Periodicity





http://functions.wolfram.com/08.07.04.0011.01









  


  








Input Form





JacobiZeta[x + I y, m] == JacobiZeta[I y + Pi FractionalPart[x/Pi], m] /; Element[x, Reals] && Element[y, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], ",", "m"]], "]"]], "\[Equal]", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "y"]], "+", RowBox[List["\[Pi]", " ", RowBox[List["FractionalPart", "[", FractionBox["x", "\[Pi]"], "]"]]]]]], ",", "m"]], "]"]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> &#918; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> x </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> &#918; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mi> frac </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> x </mi> <mi> &#960; </mi> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[List[], Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> y </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[List[], Reals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> JacobiZeta </ci> <apply> <plus /> <ci> x </ci> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> <ci> m </ci> </apply> <apply> <ci> JacobiZeta </ci> <apply> <plus /> <apply> <times /> <pi /> <apply> <ci> FractionalPart </ci> <apply> <times /> <ci> x </ci> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> <ci> m </ci> </apply> </apply> <apply> <and /> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <in /> <ci> y </ci> <reals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["JacobiZeta", "[", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "y"]], "+", RowBox[List["\[Pi]", " ", RowBox[List["FractionalPart", "[", FractionBox["x", "\[Pi]"], "]"]]]]]], ",", "m"]], "]"]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]]]


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





2007-05-02