Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7396)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-21/4

http://functions.wolfram.com/07.22.03.7396.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), -(7/4)}, z] == (1/13157235) ((E^(2 Sqrt[z]) (13157235 + 7160400 z + 6739200 z^2 + 23122800 z^3 - 4360704 z^4 + 1853952 z^5 + 8192 z^6) + 2 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-2654775 + 5309550 Sqrt[z] - 3114936 z - 849528 z^(3/2) + 1271808 z^2 + 476928 z^(5/2) + 55296 z^3 + 2048 z^(7/2)) Erf[Sqrt[2] z^(1/4)] - 2 Sqrt[2 Pi] z^(11/4) (2654775 + 5309550 Sqrt[z] + 3114936 z - 849528 z^(3/2) - 1271808 z^2 + 476928 z^(5/2) - 55296 z^3 + 2048 z^(7/2)) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

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)

2007-05-02

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