Periodic Functions Of Fourier Series
Periodic Functions Of Fourier Series : Generally, periodic functions are the functions which returns the same value in regular interval of time . But in trigonometric functions , it returns the same value in the time interval of 2π radian . For example : The best example to describe periodic functions is sine function i.e, sin(x+2π) = sinx So as discussed before Fourier series is generated by these types of periodic functions like sine and cosine functions . Theorem Related To Periodic Function of Fourier Series : For a periodic function of period 2π , prove that β β+2π (i) ∫ f dx = ∫ f dx , α α+2π π α+2π (ii) ∫ f dx = ∫ f dx , -π α π π (iii) ∫ f(x) dx = ∫ f(γ+x) dx , -π -π α,β,γ being any