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

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

For fixed z and a₁=11/4, b_1`=-1/2

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

Input Form

HypergeometricPFQ[{11/4}, {-(1/2), 23/4}, z] == -((1/(134217728 z^(19/4))) ((3135 (4 z^(1/4) (723647925 + 964863900 Sqrt[z] + 698377680 z + 343062720 z^(3/2) + 120766464 z^2 + 30670848 z^(5/2) + 5373952 z^3 + 524288 z^(7/2) + E^(4 Sqrt[z]) (-723647925 + 964863900 Sqrt[z] - 698377680 z + 343062720 z^(3/2) - 120766464 z^2 + 30670848 z^(5/2) - 5373952 z^3 + 524288 z^(7/2))) - 12285 E^(2 Sqrt[z]) Sqrt[2 Pi] (58905 - 5984 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] + 12285 E^(2 Sqrt[z]) Sqrt[2 Pi] (58905 - 5984 z + 256 z^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]