Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8501)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8501.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 3/4}, -z] == ((4 z (636296007414375 + 315118022719500 z + 213562504108800 z^2 + 5606153934796800 z^3 + 13245443133753600 z^4 + 3915857075834880 z^5 + 311814663045120 z^6 + 8615794573312 z^7 + 87056973824 z^8 + 268435456 z^9) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (1908888022243125 + 581756349636000 z + 441731877602400 z^2 + 676952843212800 z^3 + 5617110916771200 z^4 + 1867236947896320 z^5 + 153286448578560 z^6 + 4280917426176 z^7 + 43444600832 z^8 + 134217728 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (5726664066729375 + 654475893340500 z + 936098853505200 z^2 + 1756853807385600 z^3 + 13539056864256000 z^4 + 49495823062963200 z^5 + 15364454810664960 z^6 + 1238776907563008 z^7 + 34376540749824 z^8 + 347959459840 z^9 + 1073741824 z^10) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(21344906655072000 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]