Kummer confluent hypergeometric function 1F1: Transformations (formula 07.20.16.0004)

Hypergeometric1F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric1F1[a,b,z]

Transformations

Products, sums, and powers of the direct function

Products of the direct function

http://functions.wolfram.com/07.20.16.0004.01

Input Form

Hypergeometric1F1[a, b, c z] Hypergeometric1F1[\[Alpha], \[Beta], d z] == Sum[((Pochhammer[a, m] c^m)/(Pochhammer[b, m] m!)) ((Pochhammer[\[Alpha], k - m] d^(k - m))/(Pochhammer[\[Beta], k - m] (k - m)!)) z^k, {k, 0, Infinity}, {m, 0, k}]

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]