Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9665)

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/07.22.03.9665.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 15/4}, -z] == ((2 z (-298926187560000 + 3089126353438125 z - 3716232986466000 z^2 + 11593989728006400 z^3 + 4049374381977600 z^4 + 326472641740800 z^5 + 8907930992640 z^6 + 88499814400 z^7 + 268435456 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - Sqrt[z] (-1793557125360000 + 6705154595514375 z - 6841924995906000 z^2 + 9520767646790400 z^3 + 3859303878144000 z^4 + 321050714112000 z^5 + 8853069496320 z^6 + 88332042240 z^7 + 268435456 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 (-672583922010000 - 1921668348600000 z + 4944425971109625 z^2 - 5494616418891600 z^3 + 10694337932678400 z^4 + 3971077973913600 z^5 + 324279735091200 z^6 + 8885910896640 z^7 + 88432705536 z^8 + 268435456 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (14063163079680000 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]