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variants of this functions
Zeta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/10.01.27.0001.01









  


  








Input Form





Zeta[z] == RiemannSiegelZ[I/2 - I z] Exp[(-I) RiemannSiegelTheta[I/2 - I z]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Zeta", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["RiemannSiegelZ", "[", RowBox[List[FractionBox["\[ImaginaryI]", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], RowBox[List["Exp", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["RiemannSiegelTheta", "[", RowBox[List[FractionBox["\[ImaginaryI]", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;z&quot;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mrow> <semantics> <mi> Z </mi> <annotation encoding='Mathematica'> TagBox[&quot;Z&quot;, RiemannSiegelZ] </annotation> </semantics> <mo> ( </mo> <mrow> <mfrac> <mi> &#8520; </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> exp </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mrow> <semantics> <mi> &#977; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CurlyTheta]&quot;, RiemannSiegelTheta] </annotation> </semantics> <mo> ( </mo> <mrow> <mfrac> <mi> &#8520; </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <ci> RiemannSiegelZ </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <exp /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <ci> RiemannSiegelTheta </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Zeta", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["RiemannSiegelZ", "[", RowBox[List[FractionBox["\[ImaginaryI]", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["RiemannSiegelTheta", "[", RowBox[List[FractionBox["\[ImaginaryI]", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]]]]]]]


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





2001-10-29