ISSN:
1573-8876
Keywords:
Legendre-Sobolev polynomials
;
orthogonality with respect to the Legendre-Sobolev inner product
;
Legendre polynomials
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract For the Legendre-Sobolev orthonormal polynomials $$\hat B_n (x) = \hat B_n (x;M,N)$$ depending on the parametersM≥0,N≥0, weighted and uniform estimates on the orthogonality interval are obtained. It is shown that, unlike the Legendre orthonormal polynomials, the polynomials $$\hat B_n (x)$$ forM〉0,N〉0 decay at the rate ofn −3/2 at the points 1 and −1. The values of $$\hat B'_n ( \pm 1)$$ are calculated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02355461
Permalink