Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0606)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=3

http://functions.wolfram.com/07.22.03.0606.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3, 4}, -z] == (1/(23283371986875 z^2)) (16 (8 z (-21070924875 + 251290133325 z + 258121987200 z^2 + 52022190600 z^3 + 3314419200 z^4 + 79032960 z^5 + 718848 z^6 + 2048 z^7) BesselJ[0, Sqrt[z]]^2 - Sqrt[z] (-316063873125 + 961453508400 z + 1791870141600 z^2 + 397301803200 z^3 + 26050694400 z^4 + 627978240 z^5 + 5738496 z^6 + 16384 z^7) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + 2 (21070924875 - 193542841800 z + 611847828900 z^2 + 937488416400 z^3 + 201688365600 z^4 + 13101742080 z^5 + 314700288 z^6 + 2871296 z^7 + 8192 z^8) BesselJ[1, Sqrt[z]]^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]