Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7414)

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=-19/4

http://functions.wolfram.com/07.22.03.7414.01

Input Form

HypergeometricPFQ[{5}, {-(19/4), -(13/4)}, z] == (1/115540425) ((E^(2 Sqrt[z]) (115540425 + 37422000 z + 13305600 z^2 + 9031680 z^3 + 41287680 z^4 - 46373376 z^5 - 1024000 z^6) - 32 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (-502425 + 1004850 Sqrt[z] + 765600 z + 175680 z^(3/2) + 16128 z^2 + 512 z^(5/2)) Erf[Sqrt[2] z^(1/4)] - 32 Sqrt[2 Pi] z^(17/4) (502425 + 1004850 Sqrt[z] - 765600 z + 175680 z^(3/2) - 16128 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]