Complex Form Of Fourier Series

COMPLEX FORM OF FOURIER SERIES

Let f (x) be a periodic function of period 2л in the interval (c, c +2л). The Fourier series of f (x) is given by

This is called the complex form of the Fourier series.

Note: If f(x) is a periodic function of period 21 then the complex form of the Fourier series in c <x<c+21 is given by

Problems based on Complex form of Fourier Series

FORMULA

Example 2.4.1. Find the complex form of the Fourier series of eax, where 'a' is a constant in -l< x <l

Example 2.4.2. Find the complex form of the Fourier series of f(x) e^-x in -1 <x<1

Example 2.4.3. Find the Complex form of Fourier series of

Example 2.4.4. Derive the complex form of Fourier series for (x) = e^ax, -π <x<л, given that a is a real constant. Deduce that

2.4.5 : Find the complex form of the Fourier series of the function f(x) = ex when -π <x<л and f(x+2 π) = f(x)