Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7438)

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=-17/4

http://functions.wolfram.com/07.22.03.7438.01

Input Form

HypergeometricPFQ[{5}, {-(17/4), -(7/4)}, z] == (1/626535) ((-3 E^(2 Sqrt[z]) (-208845 - 140400 z - 172800 z^2 - 699080 z^3 + 466912 z^4 + 17920 z^5) - E^(4 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (530955 - 1061910 Sqrt[z] + 330372 z + 755136 z^(3/2) + 238464 z^2 + 27136 z^(5/2) + 1024 z^3) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] z^(11/4) (530955 + 1061910 Sqrt[z] + 330372 z - 755136 z^(3/2) + 238464 z^2 - 27136 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]