Kummer confluent hypergeometric function 1F1: Differentiation (formula 07.20.20.0040)

Hypergeometric1F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric1F1[a,b,z]

Differentiation

Symbolic differentiation

With respect to z

http://functions.wolfram.com/07.20.20.0040.01

Input Form

D[Hypergeometric1F1[a, b, z], {z, n}] == ((-1)^(n - 1) Pochhammer[b - 1, n] (Sum[((n - k - 1)! (-z)^k Pochhammer[a, k] Hypergeometric1F1[a + k, -1 + b, z])/(k! (n - 2 k - 1)! Pochhammer[2 - n - b, k] Pochhammer[b, k]), {k, 0, n - 1}] - Sum[((n - k)! (-z)^k Pochhammer[a, k] Hypergeometric1F1[a + k, b, z])/ (k! (n - 2 k)! Pochhammer[2 - n - b, k] Pochhammer[b - 1, k]), {k, 0, n}]))/z^n /; 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

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]