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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 Gamma(-n+Epsilon) at Epsilon==0 > For the function itself





http://functions.wolfram.com/06.05.06.0031.01









  


  










Input Form





Gamma[-n + \[Epsilon]] \[Proportional] ((-1)^n/(n! \[Epsilon])) (1 + Pi \[Epsilon] Sum[(j + 1) Sum[(((-1)^(r + j) Binomial[j, r])/(1 + r)) Subscript[p, r, j] Subscript[c, k - j] \[Epsilon]^k, {r, 0, j}], {k, 0, Infinity}, {j, 0, k + 1}]) /; Element[n, Integers] && n >= 0 && (\[Epsilon] -> 0) && Subscript[c, 2 k] == 0 && Subscript[c, 2 k + 1] == ((-1)^k 2 (2^(2 k + 1) - 1) BernoulliB[2 k + 2] Pi^(2 k + 1))/(2 k + 2)! && 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][n + 1]/(n! k!)










Standard Form





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MathML Form







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Rule Form





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





2007-05-02