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http://functions.wolfram.com/10.12.03.0009.01
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RamanujanTauTheta[-((17 I)/3) + I n] ==
(1/6) I ((69 Log[3])/2 + 31 Log[2 Pi] - 6 n Log[6 Pi] + 6 Log[Gamma[1/3]] +
3 Sum[Log[-2 + 3 k], {k, 1, n}] -
3 Sum[Log[-1 + 3 k], {k, 1, 11 - n}]) /; Element[n, Integers] &&
n >= 0 && n <= 11
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> τθ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 17 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 3 </mn> </mfrac> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> n </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mn> 69 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mn> 3 </mn> <mo> ) </mo> </mrow> </mrow> <mn> 2 </mn> </mfrac> <mo> + </mo> <mrow> <mn> 31 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> n </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </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> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </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> ∈ </mo> <mi> ℕ </mi> </mrow> <mo> ∧ </mo> <mrow> <mi> n </mi> <mo> ≤ </mo> <mn> 11 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> τθ </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 17 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> n </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 69 </cn> <apply> <ln /> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 31 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <ci> n </ci> <apply> <ln /> <apply> <times /> <cn type='integer'> 6 </cn> <pi /> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <ln /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </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'> 3 </cn> <ci> k </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </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'> 3 </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> ℕ </ci> </apply> <apply> <leq /> <ci> n </ci> <cn type='integer'> 11 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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