Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a969)

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.a969.01

Input Form

HypergeometricPFQ[{-(11/4)}, {9/2, -(17/4)}, -z] == ((4 z (162648330075 + 5996251800 z + 6681062400 z^2 - 1434337280 z^3 + 89784320 z^4 - 2097152 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-487944990225 + 74953147500 z - 3876364800 z^2 + 746987520 z^3 - 45547520 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (1463834970675 - 503685151200 z + 39975012000 z^2 + 28314316800 z^3 - 5830410240 z^4 + 361234432 z^5 - 8388608 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (10549656000 Sqrt[2] z^(11/4))

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]