Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a98d)

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`=11/2

http://functions.wolfram.com/07.22.03.a98d.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, 11/4}, -z] == ((4 z (53482275 + 48024900 z - 213617250 z^2 + 771531840 z^3 + 226897920 z^4 + 11780096 z^5 + 131072 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (160446825 + 113513400 z - 215644275 z^2 + 323991360 z^3 + 109877760 z^4 + 5849088 z^5 + 65536 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (481340475 + 248856300 z + 646153200 z^2 - 1348439400 z^3 + 2876670720 z^4 + 896016384 z^5 + 46989312 z^6 + 524288 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (1845792000 Sqrt[2] z^(15/4))

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]