Derive the Maclaurin series of fz12z2SolutionGiven fz12z2 Ta

Derive the Maclaurin series of f(z)=1/(2-z^2)

Solution

Given f(z)=1/(2-z^2)

Taking 2 out of the denominator and rewriting the equation we have

f(z)= 1/2 * 1/(1-z^2/2) = 1/2 * (1-z^2/2)^-1

= 1/2 * (1+z^2/2+z^4/4+z^6/8+z^8/16+.......)

= 1/2 + z^2/4 + z^4/8 + z^6/16+ z^8/32+....... which is Maclaurin series of given complex function