Chebyshev approximations.

[Brian Gough]

Andrea Riciputi writes:
 > Reading the reference manual's chapter about Chebyshev
 > approximation it's not clear (at least to me) how the c_n are
 > defined. In particular I've found out that I've to double all the
 > coefficients I've calculated by my own, in order to get
 > gsl_cheb_eval to work properly.  My c_n definition is: c_n = k
 > \int{0}{\pi} f(x) \cos(n x) dx where k = 2/pi if n != 0 and k =
 > 1/pi if n == 0. Given these definitions the series expansion is:
 > f(x) = \sum{k = 0}{N} c_k cos(k x) Where am I wrong?

I think it's a bug -- the implementation is different from the
definition given in the manual, there is a factor of 0.5 which needs
to be moved from the eval function to the init function.
 
Brian