Regularized confluent hypergeometric function 0F1: Representations through more general functions (formula 07.18.26.0067)

Hypergeometric0F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1Regularized[b,z]

Representations through more general functions

Through Meijer G

Generalized cases involving sin

http://functions.wolfram.com/07.18.26.0067.01

Input Form

Sin[z + a] Hypergeometric0F1Regularized[\[Nu] + 1, -(z^2/4)] == 2^(\[Nu] - 1/2) MeijerG[{{(1 - 2 \[Nu])/4, (3 - 2 \[Nu])/4}, {a/Pi}}, {{0, 1/2}, {-\[Nu], 1/2 - \[Nu], a/Pi}}, z, 1/2]

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

HypergeometricPFQRegularized[{a},{b},z]
HypergeometricPFQRegularized[{a₁,a₂},{b₁},z]
HypergeometricPFQRegularized[{a₁,...,a_p},{b₁,...,b_q},z]