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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=7/2

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

Input Form

HypergeometricPFQ[{23/4}, {7/2, -(19/4)}, z] == (1/(577899630 Sqrt[2] z^(5/4))) ((-288 z (7342755 + 15331680 z - 2429952 z^2 - 688128 z^3 + 65536 z^4) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (4088140875 + 3649408560 z + 194342400 z^2 - 443326464 z^3 + 21430272 z^4 - 1048576 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 3 (6813568125 + 4761666000 z + 1082027520 z^2 - 702750720 z^3 - 40828928 z^4 + 5242880 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]