Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8927)

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/07.22.03.8927.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(3/4)}, -z] == -((1/(4292771175 z^(1/4))) (Sqrt[2] ((-4292771175 + 3592103760 z + 51280750080 z^2 + 33229663488 z^3 + 4057804800 z^4 + 130744320 z^5 + 1048576 z^6) BesselJ[1/4, Sqrt[z]]^2 - 24 Sqrt[z] (-682568775 + 1713443760 z + 1866579120 z^2 + 246559488 z^3 + 8114176 z^4 + 65536 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (986792625 - 11645046000 z + 29984048640 z^2 + 30311850240 z^3 + 3960778752 z^4 + 129957888 z^5 + 1048576 z^6) 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]