Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6732)

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=2, b₁>=-23/4

For fixed z and a₁=2, b₁=3/4

http://functions.wolfram.com/07.22.03.6732.01

Input Form

HypergeometricPFQ[{2}, {3/4, 21/4}, z] == (1/(131072 z^(17/4))) ((1105 (8 E^(2 Sqrt[z]) z^(1/4) (12285 + 2484 z + 208 z^2) + 9 E^(4 Sqrt[z]) Sqrt[2 Pi] (-1365 + 2730 Sqrt[z] - 2460 z + 1280 z^(3/2) - 400 z^2 + 64 z^(5/2)) Erf[Sqrt[2] z^(1/4)] - 9 Sqrt[2 Pi] (1365 + 2730 Sqrt[z] + 2460 z + 1280 z^(3/2) + 400 z^2 + 64 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]