Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6284)

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=1, b₁>=-23/4

For fixed z and a₁=1, b₁=-17/4

http://functions.wolfram.com/07.22.03.6284.01

Input Form

HypergeometricPFQ[{1}, {-(17/4), -(3/4)}, z] == (1/29835) ((E^(2 Sqrt[z]) (29835 + 9360 z + 19200 z^2 + 4096 z^3) + 256 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (-15 + 30 Sqrt[z] - 24 z + 8 z^(3/2)) Erf[Sqrt[2] z^(1/4)] - 256 Sqrt[2 Pi] z^(7/4) (15 + 30 Sqrt[z] + 24 z + 8 z^(3/2)) 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]