Ramanujan tau theta function: Representations through equivalent functions (formula 10.12.27.0002)

RamanujanTauTheta

$Mathematica Notation$

Zeta Functions and Polylogarithms

RamanujanTauTheta[z]

Representations through equivalent functions

With related functions

http://functions.wolfram.com/10.12.27.0002.01

Input Form

RamanujanTauTheta[z] -> (-I) Log[RamanujanTauZ[z]/RamanujanTauL[6 + I z]]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["RamanujanTauTheta", "[", "z", "]"]], "\[Rule]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["RamanujanTauZ", "[", "z", "]"]], RowBox[List["RamanujanTauL", "[", RowBox[List["6", "+", 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> <mrow> <mi> τθ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> τZ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> τL </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Rule </ci> <apply> <ci> τθ </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <ln /> <apply> <times /> <apply> <ci> τZ </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> τL </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["RamanujanTauTheta", "[", "z", "]"]], "\[Rule]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["RamanujanTauZ", "[", "z", "]"]], RowBox[List["RamanujanTauL", "[", RowBox[List["6", "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]], "]"]]]]]]]]

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

2007-05-02