Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6902)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-13/4

http://functions.wolfram.com/07.22.03.6902.01

Input Form

HypergeometricPFQ[{3}, {-(13/4), 5/4}, z] == (1/(9360 z^(1/4))) ((8 E^(2 Sqrt[z]) z^(1/4) (-1035 + 564 z + 112 z^2) + E^(4 Sqrt[z]) Sqrt[2 Pi] (2205 - 4410 Sqrt[z] + 2100 z + 1680 z^(3/2) - 2160 z^2 + 512 z^(5/2) + 256 z^3) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (2205 + 4410 Sqrt[z] + 2100 z - 1680 z^(3/2) - 2160 z^2 - 512 z^(5/2) + 256 z^3) 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]