Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a98l)

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

For fixed z and a₁=-11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a98l.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, 19/4}, -z] == ((2 z (-711260775225 + 640215576000 z - 309794284800 z^2 + 396052234240 z^3 + 65732935680 z^4 + 2176843776 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - Sqrt[z] (-1574388290475 + 1016626010400 z - 469621152000 z^2 + 358430392320 z^3 + 64400588800 z^4 + 2166358016 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 (419545526400 - 1062755018325 z + 786420835200 z^2 - 386824838400 z^3 + 380438446080 z^4 + 65195278336 z^5 + 2172649472 z^6 + 16777216 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(409519718400 Sqrt[2] z^(15/4))

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]