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RamanujanTauZ






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RamanujanTauZ[z] > Representations through equivalent functions > With related functions





http://functions.wolfram.com/10.11.27.0002.01









  


  










Input Form





RamanujanTauZ[z] == ((E^((1/2) (-LogGamma[6 - I z] + LogGamma[6 + I z])) Sqrt[Gamma[6 - I z]])/((2 Pi)^(I z) Sqrt[I z (1 + z^2) (4 + z^2) (9 + z^2) (16 + z^2) (25 + z^2) Gamma[-5 - I z]])) RamanujanTauL[6 + I z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamanujanTauZ", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["LogGamma", "[", RowBox[List["6", "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], "+", RowBox[List["LogGamma", "[", RowBox[List["6", "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]], RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]], " ", SqrtBox[RowBox[List["Gamma", "[", RowBox[List["6", "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]], ")"]], " ", RowBox[List["RamanujanTauL", "[", RowBox[List["6", "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], SqrtBox[RowBox[List["\[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["Gamma", "[", RowBox[List[RowBox[List["-", "5"]], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]]]]]]










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





2007-05-02





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