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RamanujanTauZ






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RamanujanTauZ[z] > Differentiation > Low-order differentiation





http://functions.wolfram.com/10.11.20.0001.01









  


  










Input Form





D[RamanujanTauZ[z], z] == RamanujanTauZ[z] ((-14400 - 11 z^2 (5748 + 3475 z^2 + 651 z^4 + 45 z^6 + z^8) + z (1 + z^2) (4 + z^2) (9 + z^2) (16 + z^2) (25 + z^2) (Pi Coth[Pi z] - I Log[4 Pi^2]) + 2 I z (1 + z^2) (4 + z^2) (9 + z^2) (16 + z^2) (25 + z^2) PolyGamma[6 + I z])/(2 z (1 + z^2) (4 + z^2) (9 + z^2) (16 + z^2) (25 + z^2))) + (I Pi^(-(1/2) - I z) Gamma[6 + I z] Sqrt[Sinh[Pi z]/(14400 z + 21076 z^3 + 7645 z^5 + 1023 z^7 + 55 z^9 + z^11)] Derivative[1][RamanujanTauL][6 + I z])/2^(I z)










Standard Form





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MathML Form







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<apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <ci> D </ci> <apply> <ci> &#964;L </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='integer'> 6 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["RamanujanTauZ", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["RamanujanTauZ", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "14400"]], "-", RowBox[List["11", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["5748", "+", RowBox[List["3475", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["651", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["45", " ", SuperscriptBox["z", "6"]]], "+", SuperscriptBox["z", "8"]]], ")"]]]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["9", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["16", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["25", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["Coth", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["4", " ", SuperscriptBox["\[Pi]", "2"]]], "]"]]]]]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "z", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["9", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["16", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["25", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["PolyGamma", "[", RowBox[List["6", "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["9", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["16", "+", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["25", "+", SuperscriptBox["z", "2"]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]], " ", SuperscriptBox["\[Pi]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List["6", "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], " ", SqrtBox[FractionBox[RowBox[List["Sinh", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]], RowBox[List[RowBox[List["14400", " ", "z"]], "+", RowBox[List["21076", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["7645", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1023", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["55", " ", SuperscriptBox["z", "9"]]], "+", SuperscriptBox["z", "11"]]]]], " ", RowBox[List[SuperscriptBox["RamanujanTauL", "\[Prime]", Rule[MultilineFunction, None]], "[", RowBox[List["6", "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2007-05-02





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