Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











RamanujanTauTheta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RamanujanTauTheta[z] > Series representations > Generalized power series > Expansions at z==6i





http://functions.wolfram.com/10.12.06.0013.01









  


  








Input Form





RamanujanTauTheta[z] \[Proportional] (I/2) Log[I (z - 6 I)] + (I/2) Log[39916800] - 6 I Log[2 Pi] + (1/2) (83711/27720 - 2 EulerGamma - 2 Log[2 Pi]) (z - 6 I) + ((239437889 I)/614718720) (z - 6 I)^2 + \[Ellipsis] /; (z -> 6 I)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamanujanTauTheta", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List[FractionBox["\[ImaginaryI]", "2"], RowBox[List["Log", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["z", "-", RowBox[List["6", " ", "\[ImaginaryI]"]]]], ")"]]]], "]"]]]], "+", RowBox[List[FractionBox["\[ImaginaryI]", "2"], RowBox[List["Log", "[", "39916800", "]"]]]], "-", RowBox[List["6", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[FractionBox["83711", "27720"], "-", RowBox[List["2", " ", "EulerGamma"]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]]]], ")"]], RowBox[List["(", RowBox[List["z", "-", RowBox[List["6", "\[ImaginaryI]"]]]], ")"]]]], "+", RowBox[List[FractionBox[RowBox[List["239437889", " ", "\[ImaginaryI]", " "]], "614718720"], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", RowBox[List["6", " ", "\[ImaginaryI]"]]]], ")"]], "2"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["z", "->", RowBox[List["6", "\[ImaginaryI]"]]]], ")"]]]]]]








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> &#964;&#952; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 39916800 </mn> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mn> 83711 </mn> <mn> 27720 </mn> </mfrac> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <semantics> <mi> &#8509; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubledGamma]&quot;, Function[List[], EulerGamma]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mn> 239437889 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 614718720 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> &#964;&#952; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <imaginaryi /> <apply> <ln /> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <imaginaryi /> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <imaginaryi /> <apply> <ln /> <cn type='integer'> 39916800 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <imaginaryi /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> </apply> <cn type='rational'> 83711 <sep /> 27720 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <eulergamma /> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <imaginaryi /> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 239437889 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> 614718720 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <imaginaryi /> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <apply> <times /> <cn type='integer'> 6 </cn> <imaginaryi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamanujanTauTheta", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["z", "-", RowBox[List["6", " ", "\[ImaginaryI]"]]]], ")"]]]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", "39916800", "]"]]]], "-", RowBox[List["6", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[FractionBox["83711", "27720"], "-", RowBox[List["2", " ", "EulerGamma"]], "-", RowBox[List["2", " ", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["z", "-", RowBox[List["6", " ", "\[ImaginaryI]"]]]], ")"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["239437889", " ", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", RowBox[List["6", " ", "\[ImaginaryI]"]]]], ")"]], "2"]]], "614718720"], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", RowBox[List["6", " ", "\[ImaginaryI]"]]]], ")"]]]]]]]]


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





2007-05-02