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fourier_an takes four or five arguments : an expression expr depending of a variable, the name of this variable (for example x), the period T, an integer n and a real a (by default a = 0).
fourier_an(expr,x,T,n,a) returns the Fourier coefficient an of a function f of variable x defined on [a, a + T[ by f (x) = expr and such that f is periodic of period T:

an = $\displaystyle {\frac{{2}}{{T}}}$$\displaystyle \int_{a}^{{a+T}}$f (x)cos($\displaystyle {\frac{{2\pi

To simplify the computations, ons should input assume(n,integer) before calling fourier_an to specify that n is an integer.
Example Let the function f, of period T = 2, defined on [- 1;1[ by f (x) = x2.
Input, to have the coefficient a0 :
Output :
Input, to have the coefficient an (n $ \neq$ 0) :
Output :

giac documentation written by Renée De Graeve and Bernard Parisse