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

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=5/4, b_1`>=-11/2

For fixed z and a₁=5/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{5/4}, {11/2, -(21/4)}, -z] == (1/(56576 Sqrt[2] z^(15/4))) ((-4 z (34501160925 - 6571649700 z + 382350528 z^2 - 6474752 z^3 + 16384 z^4) BesselJ[-(1/4), Sqrt[z]]^2 + 228 Sqrt[z] (1815850575 - 691752600 z + 68037312 z^2 - 2119680 z^3 + 16384 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (-310510448325 + 177434541900 z - 31093291152 z^2 + 1642169088 z^3 - 26849280 z^4 + 65536 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^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]