Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7114)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-21/4

http://functions.wolfram.com/07.22.03.7114.01

Input Form

HypergeometricPFQ[{4}, {-(21/4), 9/4}, z] == (1/(16039296 z^(5/4))) ((24 E^(2 Sqrt[z]) z^(1/4) (-945945 - 1310904 z - 209056 z^2 + 60672 z^3) + E^(4 Sqrt[z]) Sqrt[2 Pi] (2837835 - 5675670 Sqrt[z] + 10478160 z - 13388760 z^(3/2) + 9313920 z^2 - 2794176 z^(5/2) - 473088 z^3 + 680064 z^(7/2) - 198144 z^4 + 2048 z^(9/2) + 8192 z^5) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (2837835 + 5675670 Sqrt[z] + 10478160 z + 13388760 z^(3/2) + 9313920 z^2 + 2794176 z^(5/2) - 473088 z^3 - 680064 z^(7/2) - 198144 z^4 - 2048 z^(9/2) + 8192 z^5) 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]