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variants of this functions
Zeta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s,a] > Representations through equivalent functions > Interrelations





http://functions.wolfram.com/10.02.27.0008.01









  


  










Input Form





ZetaClassical[s, a] == Zeta[s, a]/E^(UnitStep[Floor[-Re[a]]] (2 UnitStep[Im[a]] - 1) Pi I s) + UnitStep[Floor[-Re[a]]] (1 - E^((-(2 UnitStep[Im[a]] - 1)) Pi I s)) ((UnitStep[Im[a]] (1 + Floor[-Re[a]] + Floor[Re[a]]))/ ((Floor[-Re[a]] + a)^2)^(s/2) + Zeta[s, a + Floor[-Re[a]] + 1])










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ZetaClassical", "[", RowBox[List["s_", ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Zeta", "[", RowBox[List["s", ",", "a"]], "]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List["UnitStep", "[", RowBox[List["Floor", "[", RowBox[List["-", RowBox[List["Re", "[", "a", "]"]]]], "]"]], "]"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["UnitStep", "[", RowBox[List["Im", "[", "a", "]"]], "]"]]]], "-", "1"]], ")"]], " ", "\[Pi]", " ", "\[ImaginaryI]", " ", "s"]]]]], "+", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["Floor", "[", RowBox[List["-", RowBox[List["Re", "[", "a", "]"]]]], "]"]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["UnitStep", "[", RowBox[List["Im", "[", "a", "]"]], "]"]]]], "-", "1"]], ")"]]]], " ", "\[Pi]", " ", "\[ImaginaryI]", " ", "s"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["Im", "[", "a", "]"]], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["Floor", "[", RowBox[List["-", RowBox[List["Re", "[", "a", "]"]]]], "]"]], "+", RowBox[List["Floor", "[", RowBox[List["Re", "[", "a", "]"]], "]"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", RowBox[List["-", RowBox[List["Re", "[", "a", "]"]]]], "]"]], "+", "a"]], ")"]], "2"], ")"]], RowBox[List["s", "/", "2"]]]], "+", RowBox[List["Zeta", "[", RowBox[List["s", ",", RowBox[List["a", "+", RowBox[List["Floor", "[", RowBox[List["-", RowBox[List["Re", "[", "a", "]"]]]], "]"]], "+", "1"]]]], "]"]]]], ")"]]]]]]]]]]










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





2007-05-02





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