Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adq5)

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

For fixed z and a₁=11/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.adq5.01

Input Form

HypergeometricPFQ[{11/4}, {-(9/2), -(19/4)}, -z] == (1/(1306495575 z^(1/4))) (Sqrt[2] ((1306495575 + 2444904000 z + 558835200 z^2 - 484323840 z^3 + 117895680 z^4 - 27353088 z^5 + 96337920 z^6 - 2097152 z^7) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (435498525 + 234303300 z - 236728800 z^2 + 67878720 z^3 - 12149760 z^4 - 802816 z^5 + 4456448 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (1306495575 - 1039084200 z + 343450800 z^2 - 70842240 z^3 + 14837760 z^4 - 14450688 z^5 + 524288 z^6) 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]