Kummer confluent hypergeometric function 1F1: Differentiation (formula 07.20.20.0034)

Hypergeometric1F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric1F1[a,b,z]

Differentiation

Symbolic differentiation

With respect to z

http://functions.wolfram.com/07.20.20.0034.02

Input Form

D[(z Hypergeometric1F1[b + n - Floor[n/2] - 3/2, b, z^2])/E^z^2, {z, n}] == (2^(2 Floor[n/2]) (Pochhammer[3/2, Floor[n/2]]/Pochhammer[b, Floor[n/2]]) Pochhammer[n - 2 Floor[n/2] - 1/2, Floor[n/2]] z^(1 - n + 2 Floor[n/2]) Hypergeometric1F1[b - 3/2, b + Floor[n/2], z^2])/E^z^2 /; 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)

2001-10-29

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]