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 PolyGamma

 http://functions.wolfram.com/06.15.02.0004.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02