Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9181)

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`=-9/2

http://functions.wolfram.com/07.22.03.9181.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 11/4}, -z] == ((-2 Sqrt[z] (343732764375 - 713253340800 z + 442354348800 z^2 - 78344847360 z^3 + 6947143680 z^4 - 385875968 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (1031198293125 - 1319933815200 z + 510096787200 z^2 - 83530137600 z^3 + 7216496640 z^4 - 396361728 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (1031198293125 + 879955876800 z - 465677372160 z^2 + 80263249920 z^3 - 7050166272 z^4 + 390070272 z^5 - 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1594117324800 Sqrt[2] z^(5/4))

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]