Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9657)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9657.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 7/4}, -z] == ((4 z (-1844336253375 - 1245525781500 z - 1226363846400 z^2 + 58950210488400 z^3 + 45848202681600 z^4 + 6607833292800 z^5 + 282848788480 z^6 + 4056940544 z^7 + 16777216 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-5533008760125 - 2682670914000 z - 2912614135200 z^2 + 19339713300600 z^3 + 21074413852800 z^4 + 3218836008960 z^5 + 140170690560 z^6 + 2023227392 z^7 + 8388608 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (-16599026280375 - 4886293450500 z - 7040642439600 z^2 - 24527276928000 z^3 + 198475081358400 z^4 + 177198307292160 z^5 + 26154699816960 z^6 + 1127364427776 z^7 + 16210984960 z^8 + 67108864 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (173535826464000 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]