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variants of this functions
Zeta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s,a] > Specific values > Specialized values > For fixed s > For zeta^(s,a)





http://functions.wolfram.com/10.02.03.0026.01









  


  








Input Form





ZetaClassical[s, -(9/2)] == (2^s - 1) Zeta[s] + (2^s (1 + 3^(-s) + 5^(-s) + 7^(-s) + 9^(-s)))/E^(I Pi s)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ZetaClassical", "[", RowBox[List["s", ",", RowBox[List["-", FractionBox["9", "2"]]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", "s"], "-", "1"]], ")"]], RowBox[List["Zeta", "[", "s", "]"]]]], "+", RowBox[List[SuperscriptBox["2", "s"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["3", RowBox[List["-", "s"]]], "+", SuperscriptBox["5", RowBox[List["-", "s"]]], "+", SuperscriptBox["7", RowBox[List["-", "s"]]], "+", SuperscriptBox["9", RowBox[List["-", "s"]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[Pi]", " ", "s"]]]]]]]]]]]








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> <mover> <mi> &#950; </mi> <mo> ^ </mo> </mover> <mo> ( </mo> <mrow> <mi> s </mi> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[OverscriptBox[&quot;\[Zeta]&quot;, &quot;^&quot;], &quot;(&quot;, RowBox[List[TagBox[&quot;s&quot;, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;9&quot;, &quot;2&quot;]]], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2], Zeta[$CellContext`e1, $CellContext`e2]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mn> 2 </mn> <mi> s </mi> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> s </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, TagBox[&quot;s&quot;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[$CellContext`e, Zeta[$CellContext`e]]]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <msup> <mn> 2 </mn> <mi> s </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mn> 3 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> + </mo> <msup> <mn> 5 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> + </mo> <msup> <mn> 7 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> <mo> + </mo> <msup> <mn> 9 </mn> <mrow> <mo> - </mo> <mi> s </mi> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Zeta </ci> <ci> s </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <power /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> Zeta </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <ci> s </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 9 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> s </ci> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <pi /> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ZetaClassical", "[", RowBox[List["s_", ",", RowBox[List["-", FractionBox["9", "2"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", "s"], "-", "1"]], ")"]], " ", RowBox[List["Zeta", "[", "s", "]"]]]], "+", RowBox[List[SuperscriptBox["2", "s"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["3", RowBox[List["-", "s"]]], "+", SuperscriptBox["5", RowBox[List["-", "s"]]], "+", SuperscriptBox["7", RowBox[List["-", "s"]]], "+", SuperscriptBox["9", RowBox[List["-", "s"]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "\[Pi]", " ", "s"]]]]]]]]]]]


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





2001-10-29