Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9454)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.9454.01

Input Form

HypergeometricPFQ[{-(19/4)}, {3/2, -(3/4)}, z] == (1/(7518420 Sqrt[z])) ((-987525 + 987525 E^(4 Sqrt[z]) + 1784160 Sqrt[z] + 1784160 E^(4 Sqrt[z]) Sqrt[z] - 2751840 z + 2751840 E^(4 Sqrt[z]) z + 5483520 z^(3/2) + 5483520 E^(4 Sqrt[z]) z^(3/2) - 27498240 z^2 + 27498240 E^(4 Sqrt[z]) z^2 - 2305800 z^(5/2) - 2305800 E^(4 Sqrt[z]) z^(5/2) + 9655968 z^3 - 9655968 E^(4 Sqrt[z]) z^3 + 151296 z^(7/2) + 151296 E^(4 Sqrt[z]) z^(7/2) - 611328 z^4 + 611328 E^(4 Sqrt[z]) z^4 - 2048 z^(9/2) - 2048 E^(4 Sqrt[z]) z^(9/2) + 8192 z^5 - 8192 E^(4 Sqrt[z]) z^5 + 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (-14549535 + 4883760 z - 306432 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (-14549535 + 4883760 z - 306432 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML 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]