Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aak8)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.aak8.01

Input Form

HypergeometricPFQ[{-(5/4)}, {11/2, 7/4}, z] == -((1/(4922368 z^(9/2))) ((9 (-121275 + 121275 E^(4 Sqrt[z]) - 242550 Sqrt[z] - 242550 E^(4 Sqrt[z]) Sqrt[z] - 170100 z + 170100 E^(4 Sqrt[z]) z - 16800 z^(3/2) - 16800 E^(4 Sqrt[z]) z^(3/2) + 24720 z^2 - 24720 E^(4 Sqrt[z]) z^2 - 14400 z^(5/2) - 14400 E^(4 Sqrt[z]) z^(5/2) + 2560 z^3 - 2560 E^(4 Sqrt[z]) z^3 + 51200 z^(7/2) + 51200 E^(4 Sqrt[z]) z^(7/2) + 27520 z^4 - 27520 E^(4 Sqrt[z]) z^4 - 116224 z^(9/2) - 116224 E^(4 Sqrt[z]) z^(9/2) - 2048 z^5 + 2048 E^(4 Sqrt[z]) z^5 + 8192 z^(11/2) + 8192 E^(4 Sqrt[z]) z^(11/2) + 32 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (2185 - 3680 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 32 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (2185 - 3680 z + 256 z^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]