Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6818)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-21/4

http://functions.wolfram.com/07.22.03.6818.01

Input Form

HypergeometricPFQ[{3}, {-(21/4), -(3/4)}, z] == (1/626535) ((E^(2 Sqrt[z]) (626535 + 477360 z + 1319040 z^2 + 161280 z^3 - 47104 z^4) - 16 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (17325 - 34650 Sqrt[z] + 26100 z - 6000 z^(3/2) - 2928 z^2 + 1536 z^(5/2) + 256 z^3) Erf[Sqrt[2] z^(1/4)] - 16 Sqrt[2 Pi] z^(7/4) (17325 + 34650 Sqrt[z] + 26100 z + 6000 z^(3/2) - 2928 z^2 - 1536 z^(5/2) + 256 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]