Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7100)

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/07.22.03.7100.01

Input Form

HypergeometricPFQ[{4}, {-(21/4), -(19/4)}, z] == (1/41247931725) ((E^(2 Sqrt[z]) (41247931725 + 6616209600 z + 1037836800 z^2 + 232243200 z^3 + 103219200 z^4 + 176160768 z^5 - 388104192 z^6 - 2097152 z^7) - 16384 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (29295 + 12228 Sqrt[z] + 1584 z + 64 z^(3/2)) Erf[Sqrt[2] z^(1/4)] + 16384 Sqrt[2 Pi] z^(23/4) (-29295 + 12228 Sqrt[z] - 1584 z + 64 z^(3/2)) 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]