suivant: fourier_cn monter: Fourier coefficients : fourier_an précédent: fourier_an   Table des matières   Index

### fourier_bn

fourier_bn 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_bn(expr,x,T,n,a) returns the Fourier coefficient bn of a function f of variable x defined on [a, a + T[ by f (x) = expr and periodic of period T:

bn = f (x)sin()dx

To simplify the computations, one should input assume(n,integer) before calling fourier_bn to specify that n is an integer.
Examples
• Let the function f, of period T = 2, defined on [- 1;1[ by f (x) = x2.
Input, to have the coefficient bn (n 0) :
assume(n,integer);fourier_bn(x^2,x,2,n,-1)
Output :
0

• Let the function f, of period T = 2, defined on [- 1;1[ by f (x) = x3.
Input, to have the coefficient b1 :
fourier_bn(x^3,x,2,1,-1)
Output :
(2*pi^2-12)/pi^3

giac documentation written by Renée De Graeve and Bernard Parisse