Taylor Series
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A Maclaurin series is shown to the left. It is a power series in which every term is divided by n! or n factorial. Maclaurin series are used to estimate the values of complex function by substituting them with approximate infinte power series.
The way to find a maclaurin series is fhown to the left. The function evaluated at zero time x^0 plus the first derivate evaluated at 0 times x^1 divided by 1! plus the second derivative time x^2 divide by 2! and so on in that fashion.
A Taylor series is an infinite series that estimates a complex function that is centered at any value, not just 0. A Maclaurin series is a Taylor series, just one that is centered at 0. The center is denoted by a.
Taylor series can be added by adding each term to the corresponding term of the other series.
Taylor series can be multiplied in a similar fashion.
The way to find a maclaurin series is fhown to the left. The function evaluated at zero time x^0 plus the first derivate evaluated at 0 times x^1 divided by 1! plus the second derivative time x^2 divide by 2! and so on in that fashion.
A Taylor series is an infinite series that estimates a complex function that is centered at any value, not just 0. A Maclaurin series is a Taylor series, just one that is centered at 0. The center is denoted by a.
Taylor series can be added by adding each term to the corresponding term of the other series.
Taylor series can be multiplied in a similar fashion.
Common Maclaurin Series
ln|1-x| = Σx^n/n= x + x^2/2 + x^3/3 + ...
Taylor series are also differentiable and integratable. One might note that ln|1+x| is the integral of 1/(1+x) and it just so happens that every term in ln|1+x| is the integral of a term in 1/(1+x) and vice versa for the derivative.