Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6600)

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=-15/4

http://functions.wolfram.com/07.22.03.6600.01

Input Form

HypergeometricPFQ[{2}, {-(15/4), 19/4}, z] == (1/(2048 z^(15/4))) ((-16 E^(2 Sqrt[z]) z^(3/4) (7432425 + 1492920 z + 110880 z^2 + 2176 z^3) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-22297275 + 44594550 Sqrt[z] - 42702660 z + 25945920 z^(3/2) - 11143440 z^2 + 3548160 z^(5/2) - 846720 z^3 + 147456 z^(7/2) - 17152 z^4 + 1024 z^(9/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (22297275 + 44594550 Sqrt[z] + 42702660 z + 25945920 z^(3/2) + 11143440 z^2 + 3548160 z^(5/2) + 846720 z^3 + 147456 z^(7/2) + 17152 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]