10/31/12

Maclaurin Series

Maclaurin series is infinite power series of n-th term equal to:

an = (f(n)(0))*xn/n!

where f(n)(0) is value of n-th derivative of certain function f(x) for x = 0.

A Maclaurin series is a Taylor series expansion of a function about 0.

It can be proven, that if function f(x) is differentiable infinite amount of times in certain neighbourhood of x = 0 and limit of Rn at infinity equals 0 and:

Rn = (f(n)(c))*xn/n!

where c is between 0 and x, then:

f(x) = f(0) + a1 + a2 + ...

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