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 PolyGamma

 http://functions.wolfram.com/06.15.02.0005.01

 Input Form

 PolyGamma[0, z] == Sum[1/k - 1/(k + z - 1), {k, 1, Infinity}] - EulerGamma

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["0", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["(", RowBox[List[FractionBox["1", "k"], "-", FractionBox["1", RowBox[List["k", "+", "z", "-", "1"]]]]], ")"]]]], "-", "EulerGamma"]]]]]]

 MathML Form

 ψ TagBox["\[Psi]", PolyGamma] ( 0 ) ( z ) k = 1 ( 1 k - 1 k + z - 1 ) - TagBox["\[DoubledGamma]", Function[EulerGamma]] PolyGamma 0 z k 1 1 k -1 -1 1 k z -1 -1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyGamma", "[", RowBox[List["0", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], RowBox[List["(", RowBox[List[FractionBox["1", "k"], "-", FractionBox["1", RowBox[List["k", "+", "z", "-", "1"]]]]], ")"]]]], "-", "EulerGamma"]]]]]]

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

 2007-05-02