Inverse of the regularized incomplete gamma function: Differentiation (formula 06.12.20.0008)

InverseGammaRegularized

$Mathematica Notation$

Gamma, Beta, Erf

InverseGammaRegularized[a,z]

Differentiation

Low-order differentiation

With respect to z

http://functions.wolfram.com/06.12.20.0008.01

Input Form

D[InverseGammaRegularized[a, z], {z, 6}] == E^(6 w) w^(1 - 6 a) (1 - 120 a^5 + a^4 (274 + 600 w) - 3 a^3 (75 + 474 w + 400 w^2) + a^2 (85 + 3 w (399 + 874 w + 400 w^2)) + w (57 + 2 w (212 + w (437 + 60 w (5 + w)))) - a (15 + 2 w (216 + w (923 + w (1037 + 300 w))))) Gamma[a]^6 /; w == InverseGammaRegularized[a, 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

InverseGammaRegularized[a,z₁,z₂]