Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7578)

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=-1/4

http://functions.wolfram.com/07.22.03.7578.01

Input Form

HypergeometricPFQ[{5}, {-(1/4), 17/4}, z] == -((1/(4194304 z^(13/4))) ((195 (8 E^(2 Sqrt[z]) z^(1/4) (14175 + 8820 z + 3696 z^2 + 2816 z^3) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-14175 + 28350 Sqrt[z] - 31500 z + 25200 z^(3/2) - 17136 z^2 + 10752 z^(5/2) - 10752 z^3 + 12288 z^(7/2) + 4096 z^4) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (-14175 - 28350 Sqrt[z] - 31500 z - 25200 z^(3/2) - 17136 z^2 - 10752 z^(5/2) - 10752 z^3 - 12288 z^(7/2) + 4096 z^4) 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]