Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afz7)

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.afz7.01

Input Form

HypergeometricPFQ[{21/4}, {-(9/2), 19/4}, -z] == (11 (2 Sqrt[z] (-384739480125 + 465139584000 z - 127512403200 z^2 + 19661291520 z^3 - 2590310400 z^4 + 37748736 z^5 + 8388608 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (1154218440375 - 3154227804000 z + 1266302419200 z^2 - 233817292800 z^3 + 32704757760 z^4 - 2535456768 z^5 - 134217728 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 2 Sqrt[z] (-1154218440375 + 691895131200 z - 165472070400 z^2 + 24566169600 z^3 - 2902917120 z^4 + 18874368 z^5 + 8388608 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (7821066240 Sqrt[2] z^(13/4))

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]