Kummer confluent hypergeometric function 1F1: Representations through more general functions (formula 07.20.26.0035)

Hypergeometric1F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric1F1[a,b,z]

Representations through more general functions

Through Meijer G

Classical cases for the direct function itself

http://functions.wolfram.com/07.20.26.0035.01

Input Form

Hypergeometric1F1[a, b, Sqrt[z]] + Hypergeometric1F1[a, b, -Sqrt[z]] == ((2^(1 + a - b) Pi^(3/2) Gamma[b])/Gamma[a]) MeijerG[{{(1 - a)/2, 1 - a/2}, {1/2}}, {{0}, {1/2, (1 - b)/2, 1 - b/2, 1/2}}, z/4]

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)

2003-08-21

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]