Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8910)

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`=5/2

http://functions.wolfram.com/07.22.03.8910.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(19/4)}, z] == (1/(897189175575 z^(1/4))) (Sqrt[2] ((-(-897189175575 + 1223261358480 z + 469032415488 z^2 + 66393427968 z^3 + 5247664128 z^4 + 286261248 z^5 + 16777216 z^6)) BesselI[1/4, Sqrt[z]]^2 + 24 Sqrt[z] (113184667575 + 33622298640 z + 4469859072 z^2 + 345182208 z^3 + 18808832 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (1090405850625 + 1669642405200 z + 525260816640 z^2 + 70661541888 z^3 + 5478875136 z^4 + 298844160 z^5 + 16777216 z^6) 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]