ABSTRACT
To determine the value of ak numerically, as defined by {63.1), a technique may be used that is exact for trigonometric polynomials (see page 322). {That is, if f is a polynomial, then the exact value of ak will be returned.)
282 VI Numerical Methods: Techniques
11 11 1 83 = T•(x) dx = (4x3 - 3x) dx = --, 0 0 2 For our specific integrand, we can evaluate the integral in (63.1) to obtain
ak = ; 1" ( ~ V1 - cos2 6) cos(k6) dO 81" = 3 sin 0 cos( k6) dO
if k is even. 1f2(1-k2)
Therefore, we can approximate I by the series
see Piessens at al. (4].
