D02UAF obtains the Chebyshev coefficients of a function discretized on Chebyshev Gauss–Lobatto points. The set of discretization points on which the function is evaluated is usually obtained by a previous call to
D02UCF.
D02UAF computes the coefficients
, for
, of the interpolating Chebyshev series
which interpolates the function
evaluated at the Chebyshev Gauss–Lobatto points
Here
denotes the Chebyshev polynomial of the first kind of degree
with argument
defined on
. In terms of your original variable,
say, the input values at which the function values are to be provided are
where
and
are respectively the upper and lower ends of the range of
over which the function is required.
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
The Chebyshev coefficients computed should be accurate to within a small multiple of machine precision.