Maclaurin's series

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Maclaurin's series

(məˈklɔːrɪnz)
n
(Mathematics) maths an infinite sum giving the value of a function f(x) in terms of the derivatives of the function evaluated at zero: f(x) = f(0) + (f′(0)x)/1! + (f″(0)x2)/2! + …. Also called: Maclaurin series
[C18: named after Colin Maclaurin (1698–1746), British mathematician who formulated it]
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In these papers it was shown that the terms of the Maclaurin series expansion of the steady-state distribution in the service rate can be obtained at low computational cost.
In contrast to the Maclaurin series expansions in [9, 10], the terms in the Taylor series expansion around some service rate [mu] = [[mu].sub.0] [not equal to] 0cannot be obtained directly.
To obtained coefficient of Maclaurin series at [eta] = 0, we choose a particular value T = 0.1 in equation (25).
Using expansion in Maclaurin series, we obtain appoximative expressions in a form of infinitive series for average bit-error rate (BER) that converge quickly.
Expanding [f.sub.1](v) and [f.sub.2](v) in the Maclaurin series around v = 0 and consider only the first four terms, can be written [f.sub.i](v) (i = 1, 2) as