Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8591)

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`=-9/2

http://functions.wolfram.com/07.22.03.8591.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), -(3/4)}, -z] == (1/(297675 z^(1/4))) (Sqrt[2] ((297675 + 1058400 z - 726138 z^3 + 222432 z^4 - 32256 z^5 + 8192 z^6) BesselJ[1/4, Sqrt[z]]^2 - 3 Sqrt[z] (396900 + 882000 z - 511035 z^2 + 131376 z^3 - 19712 z^4 + 4096 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 z (595350 + 529200 z - 474705 z^2 + 127344 z^3 - 19200 z^4 + 4096 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]