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 PolyGamma

 http://functions.wolfram.com/06.14.07.0001.01

 Input Form

 PolyGamma[z] == Integrate[(1 - t^(z - 1))/(1 - t), {t, 0, 1}] - EulerGamma /; Re[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["PolyGamma", "[", "z", "]"]], "\[Equal]", " ", RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox[RowBox[List["1", "-", SuperscriptBox["t", RowBox[List["z", "-", "1"]]]]], RowBox[List["1", "-", "t"]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "-", "EulerGamma"]]]], "/;", " ", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]

 MathML Form

 ψ TagBox["\[Psi]", PolyGamma] ( z ) 0 1 1 - t z - 1 1 - t t - TagBox["\[DoubledGamma]", Function[EulerGamma]] /; Re ( z ) > 0 Condition PolyGamma z t 0 1 1 -1 t z -1 1 -1 t -1 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyGamma", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[FractionBox[RowBox[List["1", "-", SuperscriptBox["t", RowBox[List["z", "-", "1"]]]]], RowBox[List["1", "-", "t"]]], RowBox[List["\[DifferentialD]", "t"]]]]]], "-", "EulerGamma"]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]

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

 2001-10-29