Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.acf0)

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=5/4, b_1`>=-11/2

For fixed z and a₁=5/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.acf0.01

Input Form

HypergeometricPFQ[{5/4}, {-(9/2), 13/4}, z] == (1/(5505024 z^(9/4))) ((-4 z^(1/4) (-204417675 - 272556900 Sqrt[z] - 193818240 z - 92294400 z^(3/2) - 30222336 z^2 - 6746112 z^(5/2) - 950272 z^3 - 65536 z^(7/2) + E^(4 Sqrt[z]) (-204417675 + 272556900 Sqrt[z] - 193818240 z + 92294400 z^(3/2) - 30222336 z^2 + 6746112 z^(5/2) - 950272 z^3 + 65536 z^(7/2))) + 1514205 E^(2 Sqrt[z]) Sqrt[2 Pi] (-135 + 16 z) Erf[Sqrt[2] z^(1/4)] + 1514205 E^(2 Sqrt[z]) Sqrt[2 Pi] (-135 + 16 z) 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]