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 PolyGamma

 http://functions.wolfram.com/06.14.07.0007.01

 Input Form

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

 Standard Form

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

 MathML Form

 ψ TagBox["\[Psi]", PolyGamma] ( z ) 0 1 ( x z - 1 x - 1 - 1 log ( x ) ) x /; Re ( z ) > 0 Condition PolyGamma z x 0 1 x z -1 x -1 -1 -1 1 x -1 z 0 [/itex]

 Rule Form

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

 Contributed by

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

 2001-12-21