Inverse of the regularized incomplete gamma function: Differentiation (formula 06.12.20.0009)

InverseGammaRegularized

$Mathematica Notation$

Gamma, Beta, Erf

InverseGammaRegularized[a,z]

Differentiation

Low-order differentiation

With respect to z

http://functions.wolfram.com/06.12.20.0009.01

Input Form

D[InverseGammaRegularized[a, z], {z, 7}] == (-E^(7 w)) w^(1 - 7 a) (1 + a (-21 + a (175 + a (-735 + 4 a (406 + 9 a (-49 + 20 a))))) + 120 w - 24 a (54 + a (-229 + 6 a (79 + a (-79 + 30 a)))) w + 6 (-1 + a) (-1 + 2 a) (269 + 36 a (-27 + 25 a)) w^2 - 8 (-1 + a) (755 + 18 a (-129 + 100 a)) w^3 + 36 (-1 + a) (-229 + 300 a) w^4 - 4320 (-1 + a) w^5 + 720 w^6) Gamma[a]^7 /; 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]