Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6536)

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=2, b₁>=-23/4

For fixed z and a₁=2, b₁=-21/4

http://functions.wolfram.com/07.22.03.6536.01

Input Form

HypergeometricPFQ[{2}, {-(21/4), 13/4}, z] == (1/(148512 z^(9/4))) ((8 E^(2 Sqrt[z]) z^(1/4) (10135125 + 3783780 z + 598836 z^2 + 30976 z^3 + 256 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-10135125 + 20270250 Sqrt[z] - 19999980 z + 12972960 z^(3/2) - 6153840 z^2 + 2217600 z^(5/2) - 604800 z^3 + 119808 z^(7/2) - 15616 z^4 + 1024 z^(9/2)) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (10135125 + 20270250 Sqrt[z] + 19999980 z + 12972960 z^(3/2) + 6153840 z^2 + 2217600 z^(5/2) + 604800 z^3 + 119808 z^(7/2) + 15616 z^4 + 1024 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]