Regularized confluent hypergeometric function 1F1: Differentiation (formula 07.21.20.0004)

Hypergeometric1F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric1F1Regularized[a,b,z]

Differentiation

Low-order differentiation

With respect to b

http://functions.wolfram.com/07.21.20.0004.01

Input Form

Derivative[0, 1, 0][Hypergeometric1F1Regularized][a, b, z] == (-z) a Gamma[b] HypergeometricPFQRegularized[{{1 + a}, {1}, {1, b}}, {{2, 1 + b}, {}, {1 + b}}, z, z] - PolyGamma[b] Hypergeometric1F1Regularized[a, b, 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)

2001-10-29

HypergeometricPFQRegularized[{},{b},z]
HypergeometricPFQRegularized[{a₁,a₂},{b₁},z]
HypergeometricPFQRegularized[{a₁,...,a_p},{b₁,...,b_q},z]