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variants of this functions
GammaRegularized




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > GammaRegularized[a,z1,z2] > Series representations > Generalized power series > Expansions of Q(Epsilon-n,z1,z2) at Epsilon==0 > For the function itself





http://functions.wolfram.com/06.09.06.0006.01









  


  








Input Form





GammaRegularized[-n + \[Epsilon], Subscript[z, 1], Subscript[z, 2]] \[Proportional] (-1)^n n! Gamma[-n, Subscript[z, 1], Subscript[z, 2]] \[Epsilon] + (-1)^n n! (Gamma[-n, Subscript[z, 1]] Log[Subscript[z, 1]] - Gamma[-n, Subscript[z, 2]] Log[Subscript[z, 2]] + MeijerG[{{}, {1, 1}}, {{0, 0, -n}, {}}, Subscript[z, 1]] - MeijerG[{{}, {1, 1}}, {{0, 0, -n}, {}}, Subscript[z, 2]] - Gamma[-n, Subscript[z, 1], Subscript[z, 2]] PolyGamma[1 + n]) \[Epsilon]^2 + (((-1)^n n!)/6) (3 Gamma[-n, Subscript[z, 1]] Log[Subscript[z, 1]]^2 - 3 Gamma[-n, Subscript[z, 2]] Log[Subscript[z, 2]]^2 + 6 (EulerGamma - HarmonicNumber[n] + Log[Subscript[z, 1]]) MeijerG[{{}, {1, 1}}, {{0, 0, -n}, {}}, Subscript[z, 1]] - 6 (EulerGamma - HarmonicNumber[n] + Log[Subscript[z, 2]]) MeijerG[{{}, {1, 1}}, {{0, 0, -n}, {}}, Subscript[z, 2]] + 6 MeijerG[{{}, {1, 1, 1}}, {{0, 0, 0, -n}, {}}, Subscript[z, 1]] - 6 MeijerG[{{}, {1, 1, 1}}, {{0, 0, 0, -n}, {}}, Subscript[z, 2]] + (-6 Gamma[-n, Subscript[z, 1]] Log[Subscript[z, 1]] + 6 Gamma[-n, Subscript[z, 2]] Log[Subscript[z, 2]]) PolyGamma[1 + n] + Gamma[-n, Subscript[z, 1], Subscript[z, 2]] (-Pi^2 + 3 PolyGamma[1 + n]^2 + 3 PolyGamma[1, 1 + n])) \[Epsilon]^3 + O[\[Epsilon]^4] /; Element[n, Integers] && n >= 0








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