Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8715)

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/07.22.03.8715.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(3/2), -(23/4)}, -z] == (1/(1049344065 z^(1/4))) (Sqrt[2] ((1049344065 + 2737419300 z + 2548521360 z^2 + 905490432 z^3 - 391716864 z^4 + 44040192 z^5 - 2097152 z^6) BesselJ[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-349781355 - 446097960 z - 165876480 z^2 + 54168576 z^3 - 5734400 z^4 + 262144 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (1049344065 - 60831540 z + 312238080 z^2 - 106702848 z^3 + 11403264 z^4 - 524288 z^5) 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]