Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9577)

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`=7/2

http://functions.wolfram.com/07.22.03.9577.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, 23/4}, -z] == ((2 Sqrt[z] (57566644713703125 + 50877948851730000 z + 602241802081920000 z^2 - 831141400036147200 z^3 + 2757848795077017600 z^4 + 989101516337971200 z^5 + 81174542659092480 z^6 + 2242917821317120 z^7 + 22492743729152 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]]^2 - (172699934141109375 - 110527957850310000 z + 1388218391239680000 z^2 - 1557132374801203200 z^3 + 2253190942369382400 z^4 + 941883890230886400 z^5 + 79809700366909440 z^6 + 2228975283732480 z^7 + 22449794056192 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-172699934141109375 - 257898568317390000 z + 1018651002277708800 z^2 - 1248647100464332800 z^3 + 2538550069700198400 z^4 + 969643896392908800 z^5 + 80622472931573760 z^6 + 2237321478930432 z^7 + 22475563859968 z^8 + 68719476736 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(3368414349361152000 Sqrt[2] z^(17/4))

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]