Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.abhy)

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=1/4, b_1`>=-11/2

For fixed z and a₁=1/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.abhy.01

Input Form

HypergeometricPFQ[{1/4}, {-(11/2), 21/4}, z] == (221 (4 z^(1/4) (-337347422787375 - 449796563716500 Sqrt[z] - 317252960917200 z - 148842232862400 z^(3/2) - 49208512953600 z^2 - 11601607449600 z^(5/2) - 1926623784960 z^3 - 211679723520 z^(7/2) - 15703474176 z^4 - 536870912 z^(9/2) + E^(4 Sqrt[z]) (-337347422787375 + 449796563716500 Sqrt[z] - 317252960917200 z + 148842232862400 z^(3/2) - 49208512953600 z^2 + 11601607449600 z^(5/2) - 1926623784960 z^3 + 211679723520 z^(7/2) - 15703474176 z^4 + 536870912 z^(9/2))) + 504735 E^(2 Sqrt[z]) Sqrt[2 Pi] (668365425 - 84369600 z + 6428160 z^2 - 442368 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + 504735 E^(2 Sqrt[z]) Sqrt[2 Pi] (668365425 - 84369600 z + 6428160 z^2 - 442368 z^3 + 65536 z^4) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(15874199126016 z^(17/4))

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]