Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aggp)

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`=-5/2

http://functions.wolfram.com/07.22.03.aggp.01

Input Form

HypergeometricPFQ[{23/4}, {-(5/2), -(23/4)}, -z] == (1/(1495315292625 z^(1/4))) (Sqrt[2] ((1495315292625 + 2392504468200 z + 83947525200 z^2 - 697164209280 z^3 - 958237378560 z^4 - 2083933716480 z^5 - 1288477605888 z^6 + 78341210112 z^7 - 134217728 z^8) BesselJ[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (1495315292625 + 398750744700 z - 827482748400 z^2 + 212812427520 z^3 - 1079179960320 z^4 - 221307863040 z^5 - 224608124928 z^6 + 2634022912 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (1495315292625 - 1595002978800 z + 919425276000 z^2 - 700071482880 z^3 + 244348600320 z^4 + 166656737280 z^5 - 17634951168 z^6 + 33554432 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]