Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9090)

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`=11/2

http://functions.wolfram.com/07.22.03.9090.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 17/4}, z] == ((2 z (619386886265872725 + 851857357309358400 z + 2506976385129216000 z^2 - 2111540741646336000 z^3 + 306233929580544000 z^4 - 14391979693572096 z^5 + 261822816976896 z^6 - 1871531999232 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 - 3 Sqrt[z] (980725684803739875 + 1203169667942642400 z + 1033554676022668800 z^2 - 1863249490348646400 z^3 + 294015591088128000 z^4 - 14165620021002240 z^5 + 260191568265216 z^6 - 1867773902848 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 (193446721147680000 + 1173521318203859625 z + 1314068585086857600 z^2 + 1187014164336000000 z^3 - 1895286568373452800 z^4 + 295692138233856000 z^5 - 14197441922334720 z^6 + 260423395835904 z^7 - 1868310773760 z^8 + 4294967296 z^9) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (1766782449086054400 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]