We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely Proofs and numerical counterexamples are given in situations where the zeros of R n , and S n , respectively, interlace (or do not in general) with the zeros of
Interlacing of zeros of linear combinations of classical orthogonal polynomials from different sequences
β Scribed by Kathy Driver; Kerstin Jordaan; Norbert Mbuyi
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 158 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0168-9274
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Given {P n } nβ₯0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e., Necessary and sufficient conditions are given for the orthogonality of the sequence {Q n } nβ₯0 . An interesting interpretation in terms of the Jacobi
In this paper, starting from interlacing properties of the zeros of the orthogonai polynomials, the authors propose a new method to approximate the finite Hilbert transform. For this method they give error estimates in uniform norm.