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variants of this functions
PolyGamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > PolyGamma[nu,z] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/06.15.20.0007.01









  


  








Input Form





D[PolyGamma[\[Nu], z], {z, \[Alpha]}] == (-FDPowerConstant[z, -1, \[Alpha] + \[Nu]]) z^(-1 - \[Nu] - \[Alpha]) + z^(1 - \[Nu] - \[Alpha]) Sum[(1/k^2) Hypergeometric2F1Regularized[1, 2, 2 - \[Nu] - \[Alpha], -(z/k)], {k, 1, Infinity}] - (EulerGamma z^(-\[Nu] - \[Alpha]))/Gamma[1 - \[Nu] - \[Alpha]]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["PolyGamma", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["FDPowerConstant", "[", RowBox[List["z", ",", RowBox[List["-", "1"]], ",", RowBox[List["\[Alpha]", "+", "\[Nu]"]]]], "]"]]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]", "-", "\[Alpha]"]]]]], "+", RowBox[List[SuperscriptBox["z", RowBox[List["1", "-", "\[Nu]", "-", "\[Alpha]"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["1", ",", "2", ",", RowBox[List["2", "-", "\[Nu]", "-", "\[Alpha]"]], ",", RowBox[List["-", FractionBox["z", "k"]]]]], "]"]], SuperscriptBox["k", "2"]]]]]], "-", FractionBox[RowBox[List["EulerGamma", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "\[Alpha]"]]]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Nu]", "-", "\[Alpha]"]], "]"]]]]]]]]]


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





2001-10-29