Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9184)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.9184.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 15/4}, z] == ((2 Sqrt[z] (-69777751168125 - 38498069610000 z + 35923541472000 z^2 + 15287105433600 z^3 + 2095305523200 z^4 + 151797104640 z^5 + 7130316800 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]]^2 - (-209333253504375 - 434478214170000 z + 52797352608000 z^2 + 16976494080000 z^3 + 2205278208000 z^4 + 156704440320 z^5 + 7298088960 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (209333253504375 - 12099393306000 z + 41064607584000 z^2 + 15888357273600 z^3 + 2136534220800 z^4 + 153684541440 z^5 + 7197425664 z^6 + 268435456 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(69561483264000 Sqrt[2] z^(9/4))

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]