Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9959)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.9959.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(1/2), 21/4}, -z] == -(((2 Sqrt[z] (17695362710025 + 25472406960000 z + 8151170227200 z^2 - 8972700549120 z^3 + 4969921904640 z^4 + 39106105049088 z^5 + 9378799288320 z^6 + 429496729600 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]]^2 - 3 (29492271183375 + 63426293330400 z + 12226755340800 z^2 + 7621873459200 z^3 - 17904980459520 z^4 + 31505692753920 z^5 + 9009331437568 z^6 + 425738633216 z^7 + 4294967296 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (88476813550125 + 1528344417600 z + 4657811558400 z^2 + 6210415411200 z^3 - 16318583930880 z^4 + 32481843609600 z^5 + 9060904599552 z^6 + 426275504128 z^7 + 4294967296 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(13428735344640 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]