Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9078)

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/07.22.03.9078.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 5/4}, z] == ((4 z (5334008855175 - 3386672289000 z + 307129119897600 z^2 - 613154072250720 z^3 + 235459511400960 z^4 - 23742277042176 z^5 + 796604497920 z^6 - 9468641280 z^7 + 33554432 z^8) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (8890014758625 - 4854230280900 z + 3890331244800 z^2 - 218798213634000 z^3 + 107900813180160 z^4 - 11529504645120 z^5 + 394184491008 z^6 - 4719640576 z^7 + 16777216 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (133350221379375 - 60960101202000 z + 51477418792800 z^2 - 93367949875200 z^3 + 1830978406857600 z^4 - 873636903659520 z^5 + 92616172830720 z^6 - 3158144188416 z^7 + 37773901824 z^8 - 134217728 z^9) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (608955347800800 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]