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RamanujanTauTheta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RamanujanTauTheta[z] > Transformations > Multiple arguments > Argument involving numeric multiples of variable





http://functions.wolfram.com/10.12.16.0007.01









  


  










Input Form





RamanujanTauTheta[3 z] == RamanujanTauTheta[z] + RamanujanTauTheta[z + I/3] + RamanujanTauTheta[z + (2 I)/3] + (1/2) I (2 Log[2 Pi] + Sum[Log[I z + k], {k, 2, 5}] - Sum[Log[(-I) z + k], {k, 2, 5}] - Sum[Log[1/3 - I z + k], {k, 2, 5}] - Sum[Log[2/3 - I z + k], {k, 2, 5}] + Sum[Log[1/3 + I z + k], {k, 2, 4}] + Sum[Log[2/3 + I z + k], {k, 2, 4}]) + 3 z Log[3]










Standard Form





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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> &#964;&#952; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mrow> <mi> &#964;&#952; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> &#964;&#952; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mi> &#8520; </mi> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> &#964;&#952; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; 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</mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> &#964;&#952; </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <ci> &#964;&#952; </ci> <ci> z </ci> </apply> <apply> <ci> &#964;&#952; </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> &#964;&#952; </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <cn type='integer'> 5 </cn> </uplimit> <apply> <ln /> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <cn type='integer'> 5 </cn> </uplimit> <apply> <ln /> <apply> <plus /> <ci> k </ci> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <cn type='integer'> 4 </cn> </uplimit> <apply> <ln /> <apply> <plus /> <ci> k </ci> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <cn type='integer'> 4 </cn> </uplimit> <apply> <ln /> <apply> <plus /> <ci> k </ci> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <cn type='integer'> 5 </cn> </uplimit> <apply> <ln /> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <cn type='integer'> 5 </cn> </uplimit> <apply> <ln /> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> <apply> <ln /> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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