Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9612)

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/07.22.03.9612.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, 11/4}, z] == ((2 z (711729018000 + 12736136588175 z + 114518183551200 z^2 - 67448198188800 z^3 + 8286429265920 z^4 - 320173178880 z^5 + 4276092928 z^6 - 16777216 z^7) BesselI[-(1/4), Sqrt[z]]^2 + Sqrt[z] (-4270374108000 - 30237044762925 z - 83166922238400 z^2 + 62759844576000 z^3 - 8093308354560 z^4 + 317528801280 z^5 - 4265607168 z^6 + 16777216 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 (1601390290500 - 5978523751200 z - 25562510248275 z^2 - 100377823946400 z^3 + 65494099756800 z^4 - 8208025436160 z^5 + 319110709248 z^6 - 4271898624 z^7 + 16777216 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(156785264064000 Sqrt[2] z^(11/4))

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]