Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afy3)

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.afy3.01

Input Form

HypergeometricPFQ[{21/4}, {-(9/2), -(21/4)}, -z] == -((1/(1962730531125 Sqrt[2])) (z^(1/4) ((-1962730531125 + 4361623402500 z - 3319232061600 z^2 + 1140995419200 z^3 - 306029767680 z^4 + 143712092160 z^5 + 547474636800 z^6 - 36419141632 z^7 + 67108864 z^8) BesselJ[-(1/4), Sqrt[z]]^2 + 28 Sqrt[z] (-280390075875 + 398776996800 z - 175093261200 z^2 + 48828199680 z^3 - 13931274240 z^4 + 11731599360 z^5 - 15297675264 z^6 + 184549376 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 4 z (1962730531125 - 1221254552700 z + 388221135120 z^2 - 100887171840 z^3 + 35928023040 z^4 + 112178626560 z^5 - 8786018304 z^6 + 16777216 z^7) 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]