Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7592)

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=1/4

http://functions.wolfram.com/07.22.03.7592.01

Input Form

HypergeometricPFQ[{5}, {1/4, 23/4}, z] == (1/(134217728 z^(19/4))) ((21945 (-240 E^(2 Sqrt[z]) z^(3/4) (72765 + 21868 z + 3024 z^2 + 256 z^3) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-3274425 + 6548850 Sqrt[z] - 6597360 z + 4462920 z^(3/2) - 2283120 z^2 + 944160 z^(5/2) - 330240 z^3 + 101376 z^(7/2) - 28672 z^4 + 8192 z^(9/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (3274425 + 6548850 Sqrt[z] + 6597360 z + 4462920 z^(3/2) + 2283120 z^2 + 944160 z^(5/2) + 330240 z^3 + 101376 z^(7/2) + 28672 z^4 + 8192 z^(9/2)) 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]