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http://functions.wolfram.com/10.12.03.0001.01
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RamanujanTauTheta[x] == Im[LogGamma[6 + I x]] - Log[2 Pi] x /;
Element[x, Reals]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamanujanTauTheta", "[", "x", "]"]], "\[Equal]", RowBox[List[RowBox[List["Im", "[", RowBox[List["LogGamma", "[", RowBox[List["6", "+", RowBox[List["\[ImaginaryI]", " ", "x"]]]], "]"]], "]"]], "-", RowBox[List[RowBox[List["Log", "[", RowBox[List["2", "\[Pi]"]], "]"]], "x"]]]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]
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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> x </mi> <mo> ) </mo> </mrow> <mo>  </mo> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> logΓ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> x </mi> </mrow> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <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> <mi> x </mi> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[List[], Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> τθ </ci> <ci> x </ci> </apply> <apply> <plus /> <apply> <imaginary /> <apply> <ci> LogGamma </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> x </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> <ci> x </ci> </apply> </apply> </apply> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamanujanTauTheta", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Im", "[", RowBox[List["LogGamma", "[", RowBox[List["6", "+", RowBox[List["\[ImaginaryI]", " ", "x"]]]], "]"]], "]"]], "-", RowBox[List[RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]], " ", "x"]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
