Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7uf)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7uf.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, -(11/4)}, -z] == -(((4 z (31154452875 - 2623631472 z - 14636189952 z^2 + 4368273408 z^3 - 669843456 z^4 + 143654912 z^5 + 8388608 z^6) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (51924088125 + 9600186960 z - 9892889856 z^2 + 2555768832 z^3 - 391577600 z^4 + 68157440 z^5 + 4194304 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (778861321875 + 74770686900 z + 59500059840 z^2 - 75209997312 z^3 + 19947110400 z^4 - 3077308416 z^5 + 549453824 z^6 + 33554432 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(22306056696 Sqrt[2] z^(9/4)))

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]