Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7392)

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=-21/4

http://functions.wolfram.com/07.22.03.7392.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), -(15/4)}, z] == (1/2170943775) ((E^(2 Sqrt[z]) (2170943775 + 551350800 z + 141523200 z^2 + 58060800 z^3 + 68812800 z^4 + 293594112 z^5 + 50061312 z^6 + 131072 z^7) + 128 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (-673785 + 1347570 Sqrt[z] + 937440 z + 199744 z^(3/2) + 17152 z^2 + 512 z^(5/2)) Erf[Sqrt[2] z^(1/4)] - 128 Sqrt[2 Pi] z^(19/4) (673785 + 1347570 Sqrt[z] - 937440 z + 199744 z^(3/2) - 17152 z^2 + 512 z^(5/2)) 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]