Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7422)

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/07.22.03.7422.01

Input Form

HypergeometricPFQ[{5}, {-(19/4), 3/4}, z] == (1/25280640) ((-80 E^(2 Sqrt[z]) (-316008 - 183015 z + 203004 z^2 - 25200 z^3 + 3328 z^4) - E^(4 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (-9398025 + 18796050 Sqrt[z] - 10024560 z - 5012280 z^(3/2) + 7796880 z^2 - 2227680 z^(5/2) - 913920 z^3 + 470016 z^(7/2) + 135168 z^4 + 8192 z^(9/2)) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] z^(1/4) (9398025 + 18796050 Sqrt[z] + 10024560 z - 5012280 z^(3/2) - 7796880 z^2 - 2227680 z^(5/2) + 913920 z^3 + 470016 z^(7/2) - 135168 z^4 + 8192 z^(9/2)) 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]