[seqfan] Re: person needing help with sequences
Richard Mathar
mathar at strw.leidenuniv.nl
Sat Aug 14 21:57:10 CEST 2010
I doubt that there is any standard literature on the weight function
|x-1/2|/sqrt(1-x)+|x+1/2|/sqrt(1+x). It has two "edges" at
x=+-1/2 where it is not differentiable, so usually one would not try to
implement a set of basis functions with polynomials on
such a thing; this suffers from all the standard Gibbs phenomena.
This is the major difference to the standard case of Jacobi weights over the
same [-1,1] interval.
One can probably derive the expansion coefficients by splitting all
the integrations at x=+-0.5. So a formal definition of the associated
orthogonal polynomials is not a problem.
RJM
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