Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8802)

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`=-1/2

http://functions.wolfram.com/07.22.03.8802.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), 17/4}, z] == ((2 Sqrt[z] (-22566960541125 + 42793643692800 z + 175183658496000 z^2 + 240057719193600 z^3 - 1145686671360000 z^4 + 408617232629760 z^5 - 31971065462784 z^6 + 721554505728 z^7 - 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 + 3 (37611600901875 - 98068766796000 z + 75213070732800 z^2 + 322905410150400 z^3 + 830934790963200 z^4 - 381679828992000 z^5 + 31346047057920 z^6 - 717796409344 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (112834802705625 - 53492054616000 z + 74842562995200 z^2 + 297622215475200 z^3 + 868623630336000 z^4 - 385336265932800 z^5 + 31434127441920 z^6 - 718333280256 z^7 + 4294967296 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(214020469555200 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]