Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9o7)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a9o7.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, 5/4}, -z] == (1/(20766240 Sqrt[2] z^(13/4))) ((4 z (1658475 + 615600 z + 10702080 z^2 + 15024384 z^3 + 2531328 z^4 + 65536 z^5) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (2764125 + 780300 z + 432000 z^2 + 6453120 z^3 + 1236992 z^4 + 32768 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (41461875 + 8019000 z + 5313600 z^2 + 6912000 z^3 + 52761600 z^4 + 9928704 z^5 + 262144 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]