Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8847)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.8847.01

Input Form

HypergeometricPFQ[{-(21/4)}, {1/2, 13/4}, -z] == ((2 Sqrt[z] (-288735522075 + 47340763470000 z + 236189182521600 z^2 + 215896665600000 z^3 + 44300297502720 z^4 + 2633361260544 z^5 + 50381979648 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 - 3 (-481225870125 - 2419878661200 z + 98670085113600 z^2 + 180711407923200 z^3 + 42068739686400 z^4 + 2589673390080 z^5 + 50147098624 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-1443677610375 - 4179790414800 z + 111046980844800 z^2 + 185118248448000 z^3 + 42374062080000 z^4 + 2595839016960 z^5 + 50180653056 z^6 + 268435456 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(48587367628800 Sqrt[2] z^(7/4))

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]