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Mathematica Notation

Traditional Notation

Zeta Functions and Polylogarithms > Zeta[s] > Zeros > Sums over zeros




Input Form

Subscript[Ζ,3]3*EulerGamma*StieltjesGamma[1] + EulerGamma^3 + (3*StieltjesGamma[2])/2 - (7*Zeta[3])/8 + 1/; Subscript[Ζ,3]Limit[Sum[1/Subscript[ρ,k]^3,Abs[Subscript[ρ,k]<T]], TInfinity]&&Zeta[Subscript[ρ,k]]0&& Re[Subscript[ρ,k]]≠0

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[CapitalZeta]", "3"], "\[Equal]", RowBox[List["1", "+", SuperscriptBox["EulerGamma", "3"], "+", RowBox[List["3", " ", "EulerGamma", " ", RowBox[List["StieltjesGamma", "[", "1", "]"]]]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["StieltjesGamma", "[", "2", "]"]]]], "2"], "-", FractionBox[RowBox[List["7", " ", RowBox[List["Zeta", "[", "3", "]"]]]], "8"]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["\[CapitalZeta]", "3"], "\[Equal]", RowBox[List["Limit", "[", RowBox[List[RowBox[List[UnderscriptBox["\[Sum]", RowBox[List[RowBox[List["\[LeftBracketingBar]", SubscriptBox["\[Rho]", "k"], "\[RightBracketingBar]"]], "<", "T"]]], FractionBox["1", SubsuperscriptBox["\[Rho]", "k", "3"]]]], ",", RowBox[List["T", "\[Rule]", "\[Infinity]"]]]], "]"]]]], "\[And]", RowBox[List[RowBox[List["Zeta", "[", SubscriptBox["\[Rho]", "k"], "]"]], "\[Equal]", "0"]], "\[And]", RowBox[List[RowBox[List["Re", "[", SubscriptBox["\[Rho]", "k"], "]"]], "\[NotEqual]", "0"]]]]]]]]

MathML Form

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