Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8902)

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`=3/2

http://functions.wolfram.com/07.22.03.8902.01

Input Form

HypergeometricPFQ[{-(21/4)}, {3/2, 21/4}, z] == ((2 Sqrt[z] (-8546860188942075 + 16681983523405200 z - 15543540607795200 z^2 + 868883138500608000 z^3 - 1570931753494118400 z^4 + 551256223767330816 z^5 - 52620763160641536 z^6 + 1703748028071936 z^7 - 19752554594304 z^8 + 68719476736 z^9) BesselI[1/4, Sqrt[z]]^2 - 3 (-14244766981570125 + 37932917948125200 z - 30439433690265600 z^2 + 60447102363648000 z^3 - 1156437337286246400 z^4 + 507604262442762240 z^5 - 51158699250548736 z^6 + 1686566011404288 z^7 - 19692425052160 z^8 + 68719476736 z^9) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (42734300944710375 - 22632245162326800 z + 29144138639616000 z^2 - 108804784254566400 z^3 + 1204601669900697600 z^4 - 513409888938885120 z^5 + 51362188895453184 z^6 - 1689001257861120 z^7 + 19701014986752 z^8 - 68719476736 z^9) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (836240921749094400 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]