Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7wa)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7wa.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 9/4}, z] == ((-4 z (19538493975 - 17367550200 z - 1840559094990 z^2 + 2209826092320 z^3 - 446525291520 z^4 + 24589221888 z^5 - 430309376 z^6 + 2097152 z^7) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (32564156625 - 26051325300 z - 216531540225 z^2 + 926377618320 z^3 - 212815680000 z^4 + 12107898880 z^5 - 214237184 z^6 + 1048576 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-488462349375 + 347351004000 z - 486291405600 z^2 - 2232695064600 z^3 + 7591561971840 z^4 - 1714002554880 z^5 + 97074216960 z^6 - 1714946048 z^7 + 8388608 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (3122847937440 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]