Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

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] > Specific values > Specialized values





http://functions.wolfram.com/10.12.03.0020.01









  


  










Input Form





RamanujanTauTheta[(21 I)/4 - I n] == (I/4) (-66 Log[2] - 23 Log[Pi] + 4 n Log[8 Pi] + 4 Log[Gamma[1/4]] + 2 Sum[Log[-3 + 4 k], {k, 1, 11 - n}] - 2 Sum[Log[-1 + 4 k], {k, 1, n}]) /; Element[n, Integers] && n >= 0 && n <= 11










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamanujanTauTheta", "[", RowBox[List[FractionBox[RowBox[List["21", " ", "\[ImaginaryI]"]], "4"], "-", RowBox[List["\[ImaginaryI]", " ", "n"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[ImaginaryI]", "4"], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "66"]], " ", RowBox[List["Log", "[", "2", "]"]]]], "-", RowBox[List["23", " ", RowBox[List["Log", "[", "\[Pi]", "]"]]]], "+", RowBox[List["4", " ", "n", " ", RowBox[List["Log", "[", RowBox[List["8", " ", "\[Pi]"]], "]"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["11", "-", "n"]]], RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", "k"]]]], "]"]]]]]], "-", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", "k"]]]], "]"]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["n", "\[LessEqual]", "11"]]]]]]]]










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> <mrow> <mfrac> <mrow> <mn> 21 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 4 </mn> </mfrac> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 66 </mn> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 23 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#960; </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> n </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mn> 11 </mn> <mo> - </mo> <mi> n </mi> </mrow> </munderover> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8804; </mo> <mn> 11 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> &#964;&#952; </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 21 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -66 </cn> <apply> <ln /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 23 </cn> <apply> <ln /> <pi /> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> n </ci> <apply> <ln /> <apply> <times /> <cn type='integer'> 8 </cn> <pi /> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ln /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <apply> <plus /> <cn type='integer'> 11 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </uplimit> <apply> <ln /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> k </ci> </apply> <cn type='integer'> -3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <ln /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> <apply> <leq /> <ci> n </ci> <cn type='integer'> 11 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamanujanTauTheta", "[", RowBox[List[FractionBox[RowBox[List["21", " ", "\[ImaginaryI]"]], "4"], "-", RowBox[List["\[ImaginaryI]", " ", "n_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "66"]], " ", RowBox[List["Log", "[", "2", "]"]]]], "-", RowBox[List["23", " ", RowBox[List["Log", "[", "\[Pi]", "]"]]]], "+", RowBox[List["4", " ", "n", " ", RowBox[List["Log", "[", RowBox[List["8", " ", "\[Pi]"]], "]"]]]], "+", RowBox[List["4", " ", RowBox[List["Log", "[", RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], RowBox[List["11", "-", "n"]]], RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", "k"]]]], "]"]]]]]], "-", RowBox[List["2", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", "k"]]]], "]"]]]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]], "&&", RowBox[List["n", "\[LessEqual]", "11"]]]]]]]]]]










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





2007-05-02





© 1998-2014 Wolfram Research, Inc.