Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9525)

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`=5/2

http://functions.wolfram.com/07.22.03.9525.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, 19/4}, -z] == ((2 Sqrt[z] (-132337114284375 - 175991175360000 z - 2463876455040000 z^2 + 26206230771302400 z^3 + 16147473127833600 z^4 + 2038518566092800 z^5 + 80184019517440 z^6 + 1084479242240 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (-397011342853125 + 76996139220000 z - 6159691137600000 z^2 + 18759877110374400 z^3 + 14996137476096000 z^4 + 1990175175475200 z^5 + 79513434193920 z^6 + 1081794887680 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (397011342853125 + 769961392200000 z - 5284428358809600 z^2 + 22836855586406400 z^3 + 15667249102848000 z^4 + 2018888279654400 z^5 + 79914577428480 z^6 + 1083405500416 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(36297568419840000 Sqrt[2] z^(13/4))

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]