Confluent hypergeometric function 0F1: Identities (formula 07.17.17.0009)

Hypergeometric0F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1[b,z]

Identities

Functional identities

Division on even and odd parts and generalization

http://functions.wolfram.com/07.17.17.0009.01

Input Form

Hypergeometric0F1[b, z] == Sum[(z^k/(Pochhammer[b, k] k!)) HypergeometricPFQ[{1}, {(k + 1)/n, \[Ellipsis], (k + n)/n, (b + k)/n, \[Ellipsis], (b + k + n - 1)/n}, z^n/n^(2 n)], {k, 0, n - 1}]

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},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]