Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.acy1)

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=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.acy1.01

Input Form

HypergeometricPFQ[{7/4}, {-(3/2), -(23/4)}, -z] == (1/(13627845 z^(1/4))) (Sqrt[2] (-3 (-4542615 - 8163540 z - 1718640 z^2 + 633600 z^3 - 1658880 z^4 + 65536 z^5) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-13627845 - 6320160 z + 6732000 z^2 - 4631040 z^3 + 1253376 z^4 + 131072 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 12 z (-4542615 + 3950100 z - 1869120 z^2 + 711680 z^3 + 16384 z^4) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]