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]

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</mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mn> 4 </mn> </munderover> <mrow> <mi> log </mi> <mo> &#8289; </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> <mo> - </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mn> 5 </mn> </munderover> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mn> 5 </mn> </munderover> <mrow> <mi> log </mi> <mo> &#8289; 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2007-05-02