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variants of this functions
InverseGammaRegularized






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > InverseGammaRegularized[a,z] > Series representations > Generalized power series > Expansions at generic point a==a0 > For the function itself





http://functions.wolfram.com/06.12.06.0003.01









  


  










Input Form





InverseGammaRegularized[a, z] \[Proportional] InverseGammaRegularized[Subscript[a, 0], z] + E^w w^(1 - Subscript[a, 0]) ((w^Subscript[a, 0]/Subscript[a, 0]^2) HypergeometricPFQ[ {Subscript[a, 0], Subscript[a, 0]}, {1 + Subscript[a, 0], 1 + Subscript[a, 0]}, -w] + (-1 + z) Gamma[Subscript[a, 0]] Log[w] + (Gamma[Subscript[a, 0]] - Gamma[Subscript[a, 0], w]) PolyGamma[Subscript[a, 0]]) (a - Subscript[a, 0]) + (1/2) (E^w w Gamma[Subscript[a, 0]]^3 (E^w (1 - Subscript[a, 0] + w) Gamma[Subscript[a, 0]] HypergeometricPFQRegularized[ {Subscript[a, 0], Subscript[a, 0]}, {1 + Subscript[a, 0], 1 + Subscript[a, 0]}, -w]^2 - 2 HypergeometricPFQRegularized[ {Subscript[a, 0], Subscript[a, 0], Subscript[a, 0]}, {1 + Subscript[a, 0], 1 + Subscript[a, 0], 1 + Subscript[a, 0]}, -w]) + 2 E^(2 w) w^(1 - Subscript[a, 0]) (1 - Subscript[a, 0] + w) Gamma[Subscript[a, 0]]^2 HypergeometricPFQRegularized[ {Subscript[a, 0], Subscript[a, 0]}, {1 + Subscript[a, 0], 1 + Subscript[a, 0]}, -w] ((-Gamma[Subscript[a, 0], w]) PolyGamma[Subscript[a, 0]] + Gamma[Subscript[a, 0]] ((z - 1) Log[w] + PolyGamma[Subscript[a, 0]])) + E^w w^(1 - 2 Subscript[a, 0]) (E^w (1 - Subscript[a, 0] + w) Gamma[Subscript[a, 0]]^2 ((z - 1) Log[w] + PolyGamma[ Subscript[a, 0]])^2 + Gamma[Subscript[a, 0], w] ((-w^Subscript[a, 0] + E^w (1 - Subscript[a, 0] + w) Gamma[Subscript[a, 0], w]) PolyGamma[Subscript[a, 0]]^2 + 2 Subscript[a, 0] E^w Gamma[Subscript[a, 0]] PolyGamma[Subscript[a, 0]] ((z - 1) Log[w] + PolyGamma[Subscript[a, 0]]) + w^Subscript[a, 0] (Log[w]^2 - PolyGamma[1, Subscript[a, 0]])) + Gamma[Subscript[a, 0]] (2 (z - 1) (w^Subscript[a, 0] - E^w (1 + w) Gamma[Subscript[a, 0], w]) Log[w] PolyGamma[Subscript[a, 0]] + (w^Subscript[a, 0] - 2 E^w (1 + w) Gamma[Subscript[a, 0], w]) PolyGamma[Subscript[aa, 0]]^2 + w^Subscript[a, 0] ((1 - 2 z) Log[w]^2 + PolyGamma[1, Subscript[a, 0]])))) (a - Subscript[a, 0])^2 \[Ellipsis] /; (a -> Subscript[a, 0]) && w == InverseGammaRegularized[Subscript[a, 0], z]










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





© 1998- Wolfram Research, Inc.