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http://functions.wolfram.com/10.12.06.0011.01
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RamanujanTauTheta[z] ==
z Sum[(((-1)^k PolyGamma[2 k, 6])/(2 k + 1)! - Log[2 Pi] KroneckerDelta[k])
z^(2 k), {k, 0, Infinity}] /; Abs[z] < 6
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamanujanTauTheta", "[", "z", "]"]], "\[Equal]", RowBox[List["z", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["2", "k"]], ",", "6"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "k"]], "+", "1"]], ")"]], "!"]]], "-", RowBox[List[RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]], " ", RowBox[List["KroneckerDelta", "[", "k", "]"]]]]]], ")"]], SuperscriptBox["z", RowBox[List["2", "k"]]]]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "6"]]]]]]
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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> <mi> z </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> ∞ </mi> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> ⁢ </mo> <mrow> <msup> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> </msup> <mo> ( </mo> <mn> 6 </mn> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mfrac> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <semantics> <mi> δ </mi> <annotation-xml encoding='MathML-Content'> <ci> KroneckerDelta </ci> </annotation-xml> </semantics> <mi> k </mi> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </msup> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> < </mo> <mn> 6 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> τθ </ci> <ci> z </ci> </apply> <apply> <times /> <ci> z </ci> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <ci> PolyGamma </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <factorial /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <apply> <ci> KroneckerDelta </ci> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <abs /> <ci> z </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamanujanTauTheta", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["z", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["PolyGamma", "[", RowBox[List[RowBox[List["2", " ", "k"]], ",", "6"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], ")"]], "!"]]], "-", RowBox[List[RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]], " ", RowBox[List["KroneckerDelta", "[", "k", "]"]]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["2", " ", "k"]]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "6"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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