Re: Chebyshev approximations.

[Brian Gough <bjg at network-theory dot co dot uk>]

 > > 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.
 > >

I looked at it closer and it's just c[0] that follows a different
convention.  The series is c[0]/2 + sum_{n=1} c_n T_n(x), as opposed
to sum c_n T_n(x).  I've added that to the manual to make it clearer.

-- 
Brian Gough

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