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variants of this functions
Gamma






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Gamma[z] > Series representations > Generalized power series > Expansions of 1/Gamma(z) > For the function itself





http://functions.wolfram.com/06.05.06.0039.01









  


  










Input Form





1/Gamma[z + \[Epsilon]] \[Proportional] (1/Gamma[z]) Sum[(k + 1) Sum[(((-1)^r Binomial[k, r])/(1 + r)) Subscript[p, r, k] \[Epsilon]^k, {r, 0, k}], {k, 0, Infinity}] /; (\[Epsilon] -> 0) && Subscript[p, j, 0] == 1 && Subscript[p, j, k] == (1/k) Sum[(j m - k + m) Subscript[b, m] Subscript[p, j, k - m], {m, 1, k}] && Subscript[b, k] == Derivative[k][Gamma][z]/(Gamma[z] k!) && Element[k, Integers] && k >= 0 && Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox["1", RowBox[List["Gamma", "[", RowBox[List["z_", "+", "\[Epsilon]_"]], "]"]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["r", "=", "0"]], "k"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "r"], " ", RowBox[List["Binomial", "[", RowBox[List["k", ",", "r"]], "]"]]]], ")"]], " ", SubscriptBox["p", RowBox[List["r", ",", "k"]]], " ", SuperscriptBox["\[Epsilon]", "k"]]], RowBox[List["1", "+", "r"]]]]]]]]], RowBox[List["Gamma", "[", "z", "]"]]], "/;", RowBox[List[RowBox[List["(", RowBox[List["\[Epsilon]", "\[Rule]", "0"]], ")"]], "&&", RowBox[List[SubscriptBox["p", RowBox[List["j", ",", "0"]]], "\[Equal]", "1"]], "&&", RowBox[List[SubscriptBox["p", RowBox[List["j", ",", "k"]]], "\[Equal]", FractionBox[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "k"], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["j", " ", "m"]], "-", "k", "+", "m"]], ")"]], " ", SubscriptBox["b", "m"], " ", SubscriptBox["p", RowBox[List["j", ",", RowBox[List["k", "-", "m"]]]]]]]]], "k"]]], "&&", RowBox[List[SubscriptBox["b", "k"], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["Gamma", TagBox[RowBox[List["(", "k", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]], RowBox[List[RowBox[List["Gamma", "[", "z", "]"]], " ", RowBox[List["k", "!"]]]]]]], "&&", RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", "\[GreaterEqual]", "0"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]










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





2007-05-02





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