Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9649)

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/07.22.03.9649.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, -(1/4)}, -z] == -(((4 z (-5309452850625 - 1437145132500 z - 633090427200 z^2 - 1792069171200 z^3 + 5991100416000 z^4 + 4038879559680 z^5 + 400696279040 z^6 + 10330570752 z^7 + 67108864 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-15928358551875 - 1277462340000 z - 920436501600 z^2 - 1015776115200 z^3 + 2015071027200 z^4 + 1902507909120 z^5 + 197176197120 z^6 + 5144313856 z^7 + 33554432 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (-47785075655625 + 5269532152500 z - 1558504054800 z^2 - 2447418758400 z^3 - 9117210009600 z^4 + 20480547225600 z^5 + 15770469335040 z^6 + 1592559403008 z^7 + 41255174144 z^8 + 268435456 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(5258661408000 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]