Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6846)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-19/4

http://functions.wolfram.com/07.22.03.6846.01

Input Form

HypergeometricPFQ[{3}, {-(19/4), 11/4}, z] == (1/(401280 z^(7/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (-135135 - 48180 z + 7776 z^2 + 1856 z^3) - E^(4 Sqrt[z]) Sqrt[2 Pi] (405405 - 810810 Sqrt[z] + 914760 z - 748440 z^(3/2) + 393120 z^2 - 76608 z^(5/2) - 48384 z^3 + 42624 z^(7/2) - 14336 z^4 + 2048 z^(9/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (405405 + 810810 Sqrt[z] + 914760 z + 748440 z^(3/2) + 393120 z^2 + 76608 z^(5/2) - 48384 z^3 - 42624 z^(7/2) - 14336 z^4 - 2048 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]