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 PolyGamma

 http://functions.wolfram.com/06.14.06.0016.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29