Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag3b)

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`=-3/2

http://functions.wolfram.com/07.22.03.ag3b.01

Input Form

HypergeometricPFQ[{21/4}, {-(3/2), 23/4}, -z] == -((1/(695205888 Sqrt[2] z^(17/4))) (1463 (2 Sqrt[z] (-6030399375 + 7020533520 z - 1657393920 z^2 + 188977152 z^3 - 14614528 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]]^ 2 + (18091198125 - 48629140560 z + 17589761280 z^2 - 2636255232 z^3 + 232587264 z^4 - 17825792 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (18091198125 - 10034584560 z + 2063722752 z^2 - 223506432 z^3 + 17104896 z^4 - 1048576 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^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]