Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9019)

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`=9/2

http://functions.wolfram.com/07.22.03.9019.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, -(7/4)}, -z] == ((4 z (-392546106225 + 357838689600 z + 600620832000 z^2 - 361989734400 z^3 + 409264128000 z^4 + 97711423488 z^5 + 3875536896 z^6 + 33554432 z^7) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-654243510375 - 232619914800 z + 555710803200 z^2 - 299400192000 z^3 + 164634624000 z^4 + 47184936960 z^5 + 1923088384 z^6 + 16777216 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-9813652655625 - 2616974041500 z - 1970427513600 z^2 + 4243388083200 z^3 - 2334508646400 z^4 + 1358777548800 z^5 + 379351203840 z^6 + 15401484288 z^7 + 134217728 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(1064607251400 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]