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http://functions.wolfram.com/10.12.06.0020.01
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RamanujanTauTheta[z] \[Proportional] (-(I/2)) Log[(-I) (z + 6 I)] +
I (6 Log[2 Pi] - (1/2) Log[11!]) (1 + O[z + 6 I])
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Cell[BoxData[RowBox[List[RowBox[List["RamanujanTauTheta", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[ImaginaryI]", "2"]]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["6", "\[ImaginaryI]"]]]], ")"]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", RowBox[List["(", RowBox[List[RowBox[List["6", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Log", "[", RowBox[List["11", "!"]], "]"]]]]]], ")"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "+", RowBox[List["6", "\[ImaginaryI]"]]]], "]"]]]], ")"]]]]]]]]]]
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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> <mi> τθ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </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> <mfrac> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 11 </mn> <mo> ! </mo> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> τθ </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> <apply> <ln /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 6 </cn> <imaginaryi /> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <apply> <factorial /> <cn type='integer'> 11 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 6 </cn> <imaginaryi /> </apply> </apply> </apply> </apply> </apply> </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[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["-", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["6", " ", "\[ImaginaryI]"]]]], ")"]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]], "-", FractionBox[RowBox[List["Log", "[", RowBox[List["11", "!"]], "]"]], "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "+", RowBox[List["6", " ", "\[ImaginaryI]"]]]], "]"]]]], ")"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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