Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6538)

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=-21/4

http://functions.wolfram.com/07.22.03.6538.01

Input Form

HypergeometricPFQ[{2}, {-(21/4), 17/4}, z] == (1/(91392 z^(13/4))) ((-8 E^(2 Sqrt[z]) z^(1/4) (310134825 + 103783680 z + 15135120 z^2 + 757344 z^3 + 10496 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (310134825 - 620269650 Sqrt[z] + 599999400 z - 372972600 z^(3/2) + 166486320 z^2 - 56216160 z^(5/2) + 14636160 z^3 - 2914560 z^(7/2) + 426240 z^4 - 41472 z^(9/2) + 2048 z^5) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (310134825 + 620269650 Sqrt[z] + 599999400 z + 372972600 z^(3/2) + 166486320 z^2 + 56216160 z^(5/2) + 14636160 z^3 + 2914560 z^(7/2) + 426240 z^4 + 41472 z^(9/2) + 2048 z^5) 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]