Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8z5)

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`=-3/2

http://functions.wolfram.com/07.22.03.a8z5.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(3/2), 15/4}, -z] == (1/(35389440 Sqrt[2] z^(9/4))) ((2 Sqrt[z] (-16081065 + 6486480 z + 16298496 z^2 - 11296768 z^3 + 4128768 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]]^2 - (-48243195 + 92972880 z + 18095616 z^2 - 12115968 z^3 + 3473408 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (48243195 + 9945936 z + 18805248 z^2 - 11919360 z^3 + 3866624 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]