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Next, let's discuss the discrete setup. Since we seek an even
extension of the upper semi-circle we consider the case of even
number of grid points - equally distributed along the unit circle.
There are two main choices: one
choice is to consider only the interior points,
(here,
and ).
This yields
the so called
Gauss-Chebyshev points, consult §2.5.1 below,
The second choice takes into
account also the -boundaries, considering
(here, and
r=0),
which yield the so called Gauss-Lobatto-Chebyshev points - consult
§2.5.2 below,