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RiemannSiegelTheta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelTheta[z] > Specific values > Values at fixed points





http://functions.wolfram.com/10.03.03.0008.01









  


  








Input Form





RiemannSiegelTheta[(3 I)/2] == (-(1/2)) (Pi + I Log[2 Pi^2])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["RiemannSiegelTheta", "[", FractionBox[RowBox[List["3", "\[ImaginaryI]"]], "2"], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]], "]"]]]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mi> &#977; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[CurlyTheta]&quot;, RiemannSiegelTheta] </annotation> </semantics> <mo> ( </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> RiemannSiegelTheta </ci> <apply> <times /> <cn type='integer'> 3 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <pi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RiemannSiegelTheta", "[", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]"]], "2"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["2", " ", SuperscriptBox["\[Pi]", "2"]]], "]"]]]]]], ")"]]]]]]]]


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





2001-10-29