Kummer confluent hypergeometric function 1F1: Series representations (formula 07.20.06.0004)

Hypergeometric1F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric1F1[a,b,z]

Series representations

Generalized power series

Expansions at z==infinity for polynomial cases

http://functions.wolfram.com/07.20.06.0004.01

Input Form

Hypergeometric1F1[-n, b, z] == (1/Pochhammer[b, n]) (-z)^n HypergeometricPFQ[{-n, 1 - n - b}, {}, -(1/z)] /; Element[n, Integers] && n >= 0 && !(Element[-b, Integers] && -b >= 0 && b + 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]