Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag63)

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`=3/2

http://functions.wolfram.com/07.22.03.ag63.01

Input Form

HypergeometricPFQ[{21/4}, {3/2, -(21/4)}, -z] == -((1/(2076963525 Sqrt[2])) (z^(1/4) ((-2076963525 + 5101160400 z + 3056094720 z^2 + 28876800 z^3 - 29949952 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + 16 Sqrt[z] (-956467575 - 237242880 z + 170472960 z^2 + 26443776 z^3 + 1900544 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - (-5246720325 + 3137173200 z + 3663797760 z^2 + 137797632 z^3 - 22609920 z^4 + 1048576 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]