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http://functions.wolfram.com/10.12.20.0001.01
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D[RamanujanTauTheta[z], z] == (1/2) (-2 Log[2 Pi] + PolyGamma[6 - I z] +
PolyGamma[6 + I z])
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Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["RamanujanTauTheta", "[", "z", "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]], "+", RowBox[List["PolyGamma", "[", RowBox[List["6", "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "+", RowBox[List["PolyGamma", "[", RowBox[List["6", "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], ")"]]]]]]]]
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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> <mfrac> <mrow> <mo> ∂ </mo> <mrow> <mi> τθ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <mi> z </mi> </mrow> </mfrac> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <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> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> τθ </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> </apply> </apply> <apply> <ci> PolyGamma </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <ci> PolyGamma </ci> <apply> <plus /> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["RamanujanTauTheta", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Log", "[", RowBox[List["2", " ", "\[Pi]"]], "]"]]]], "+", RowBox[List["PolyGamma", "[", RowBox[List["6", "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "+", RowBox[List["PolyGamma", "[", RowBox[List["6", "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
