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 Zeta

 http://functions.wolfram.com/10.02.27.0009.01

 Input Form

 Zeta[s, a] == Zeta[s] - HarmonicNumber[a - 1, s] /; Inequality[-(Pi/2), Less, Arg[a], LessEqual, Pi/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Zeta", "[", RowBox[List["s", ",", "a"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Zeta", "[", "s", "]"]], "-", RowBox[List["HarmonicNumber", "[", RowBox[List[RowBox[List["a", "-", "1"]], ",", "s"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "a", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 ζ ( s , a ) TagBox[RowBox[List["\[Zeta]", "(", RowBox[List[TagBox["s", Rule[Editable, True]], ",", TagBox["a", Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[List[\$CellContext`e1, \$CellContext`e2], Zeta[\$CellContext`e1, \$CellContext`e2]]]] ζ ( s ) TagBox[RowBox[List["\[Zeta]", "(", TagBox["s", Rule[Editable, True]], ")"]], InterpretTemplate[Function[\$CellContext`e, Zeta[\$CellContext`e]]]] - H HarmonicNumber a - 1 ( s ) /; - π 2 < arg ( a ) π 2 Condition Zeta s a Zeta s -1 HarmonicNumber a -1 s Inequality -1 2 -1 a 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Zeta", "[", RowBox[List["s_", ",", "a_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Zeta", "[", "s", "]"]], "-", RowBox[List["HarmonicNumber", "[", RowBox[List[RowBox[List["a", "-", "1"]], ",", "s"]], "]"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "a", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2007-05-02