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

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.acsc.01

Input Form

HypergeometricPFQ[{5/4}, {11/2, 13/4}, z] == (1/(13312 z^(9/2))) ((945 (-525 + 525 E^(4 Sqrt[z]) - 1050 Sqrt[z] - 1050 E^(4 Sqrt[z]) Sqrt[z] - 660 z + 660 E^(4 Sqrt[z]) z + 80 z^(3/2) + 80 E^(4 Sqrt[z]) z^(3/2) - 272 z^2 + 272 E^(4 Sqrt[z]) z^2 + 16 z^(5/2) + 16 E^(4 Sqrt[z]) z^(5/2) - 64 z^3 + 64 E^(4 Sqrt[z]) z^3 - 4 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (65 + 16 z) Erf[Sqrt[2] z^(1/4)] - 4 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (65 + 16 z) 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]