Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9285)

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/07.22.03.9285.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(5/2), 19/4}, -z] == ((-2 Sqrt[z] (132337114284375 - 85795697988000 z - 15084957888000 z^2 - 24338587852800 z^3 + 13819222425600 z^4 - 3325191782400 z^5 + 795072266240 z^6 + 217432719360 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 + (397011342853125 - 862356759264000 z - 80453108736000 z^2 - 28605549772800 z^3 + 15373910016000 z^4 - 3506857574400 z^5 + 666391019520 z^6 + 214748364800 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 2 Sqrt[z] (-397011342853125 + 15399227844000 z - 15755400460800 z^2 - 27917916364800 z^3 + 14640906240000 z^4 - 3446931456000 z^5 + 742391808000 z^6 + 216358977536 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(50054823936000 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]