Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8006)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.8006.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), -(11/4)}, z] == (1/436590) ((218295 + 218295 E^(4 Sqrt[z]) + 436590 Sqrt[z] - 436590 E^(4 Sqrt[z]) Sqrt[z] + 335160 z + 335160 E^(4 Sqrt[z]) z + 88200 z^(3/2) - 88200 E^(4 Sqrt[z]) z^(3/2) - 18000 z^2 - 18000 E^(4 Sqrt[z]) z^2 + 1632 z^(5/2) - 1632 E^(4 Sqrt[z]) z^(5/2) + 4224 z^3 + 4224 E^(4 Sqrt[z]) z^3 - 21504 z^(7/2) + 21504 E^(4 Sqrt[z]) z^(7/2) + 1984 z^4 + 1984 E^(4 Sqrt[z]) z^4 - 11008 z^(9/2) + 11008 E^(4 Sqrt[z]) z^(9/2) - 1024 z^5 - 1024 E^(4 Sqrt[z]) z^5 + 4096 z^(11/2) - 4096 E^(4 Sqrt[z]) z^(11/2) + 16 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-1311 - 736 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] + 16 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-1311 - 736 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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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]