I'm having trouble finding a definite answer to this question: When finding the Fourier series of a function is it always possible to find ##a_0## by first finding ##a_n## and just plugging in ##n=0##?
To help answer this, suppose you had two periodic functions f(x) and g(x) with f(x) = g(x) + C where C is a constant. How would the coefficient ##a_0## compare for the two functions? How would the coefficients ##a_n## for ##n \neq 0## compare for the two functions?