Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7608)

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, b₁>=-23/4

For fixed z and a₁=5, b₁=5/4

http://functions.wolfram.com/07.22.03.7608.01

Input Form

HypergeometricPFQ[{5}, {5/4, 15/4}, z] == (1/(4194304 z^(11/4))) ((77 (16 E^(2 Sqrt[z]) z^(3/4) (105 + 120 z + 128 z^2) + E^(4 Sqrt[z]) Sqrt[2 Pi] (315 - 630 Sqrt[z] + 900 z - 960 z^(3/2) + 1920 z^2 + 4608 z^(5/2) + 1024 z^3) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (315 + 630 Sqrt[z] + 900 z + 960 z^(3/2) + 1920 z^2 - 4608 z^(5/2) + 1024 z^3) 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]