Fourier Series
Fourier Series Definition : If the numbers a₀,a₁....aₙ,....,b₁,...bₙ.... are derived from a function f by means of Euler_Fourier formulas : π aₙ = 1/π ∫ f(x) cosnx dx ,n=0,1,2... -π .......(1) π bₙ = 1/π ∫ f(x) sinnx dx , n=0,1,2... -π then the series ∞ 1/2 a₀ = Σ (aₙcosnx + bₙsinnx) ....(2) n=1 is called the Fourier Series of f or the Fourier Series Generated by f , and the co_efficient aₙ,bₙ defined by equation(1) as the Fourier Co_efficients of f . ∞ Where 1/2 a₀+ Σ (aₙcosnx + bₙsinnx) n=1 is called Trigonometric Series . Explanation : It is to be noted that the Fourier Co_efficients have been obtained purely