Regularized confluent hypergeometric function 0F1: Identities (formula 07.18.17.0003)

Hypergeometric0F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1Regularized[b,z]

Identities

Recurrence identities

Distant neighbors

Increasing

http://functions.wolfram.com/07.18.17.0003.01

Input Form

Hypergeometric0F1Regularized[b, z] == Pochhammer[b, n] Sum[(((n - k)! (-z)^k)/(k! Pochhammer[b, k] Pochhammer[1 - b - n, k] (n - 2 k)!)) Hypergeometric0F1Regularized[ b + n, z], {k, 0, n - 1}] + z Pochhammer[b, n + 1] Sum[(((n - k - 1)! (-z)^k)/(k! Pochhammer[b, k] Pochhammer[-b - n, k + 2] (n - 2 k - 1)!)) Hypergeometric0F1Regularized[b + n + 1, z], {k, 0, n - 1}] /; 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

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