Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8711)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.8711.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(5/2), 21/4}, -z] == -(((2 Sqrt[z] (20978656827403275 + 27732469424259600 z + 5321973142886400 z^2 - 715899185971200 z^3 - 1735233123778560 z^4 + 625582075281408 z^5 - 113661746085888 z^6 + 85165980254208 z^7 + 6043018985472 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]]^2 - 3 (34964428045672125 + 71084375650688400 z + 4336422560870400 z^2 + 2928493157990400 z^3 - 2673612826214400 z^4 + 816133240258560 z^5 - 179709350510592 z^6 + 79979807244288 z^7 + 5982889443328 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (104893284137016375 - 10519212540236400 z + 1351612226764800 z^2 + 1945502447616000 z^3 - 2454017281228800 z^4 + 778103653662720 z^5 - 171794799525888 z^6 + 80701361750016 z^7 + 5991479377920 z^8 + 68719476736 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(2783410598707200 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]