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 HarmonicNumber

 http://functions.wolfram.com/06.17.06.0014.01

 Input Form

 HarmonicNumber[z, r] == Sum[1/k^r - 1/(k + z)^r, {k, 1, Infinity}] /; Re[r] > 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HarmonicNumber", "[", RowBox[List["z", ",", "r"]], "]"]], "\[Equal]", " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["(", RowBox[List[FractionBox["1", SuperscriptBox["k", "r"]], "-", FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["k", "+", "z"]], ")"]], "r"]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "r", "]"]], ">", "1"]]]]]]

 MathML Form

 H HarmonicNumber z ( r ) k = 1 ( 1 k r - 1 ( k + z ) r ) /; Re ( r ) > 1 Condition HarmonicNumber z r k 1 1 k r -1 -1 1 k z r -1 r 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HarmonicNumber", "[", RowBox[List["z_", ",", "r_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["(", RowBox[List[FractionBox["1", SuperscriptBox["k", "r"]], "-", FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["k", "+", "z"]], ")"]], "r"]]]], ")"]]]], "/;", RowBox[List[RowBox[List["Re", "[", "r", "]"]], ">", "1"]]]]]]]]

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

 2001-10-29