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Constructing Bispectral Orthogonal Polynomials from the Classical Discrete Families of Charlier, Meixner and Krawtchouk.
- Source :
-
Constructive Approximation . Feb2015, Vol. 41 Issue 1, p49-91. 43p. - Publication Year :
- 2015
-
Abstract
- Given a sequence of polynomials $$(p_n)_n$$ , an algebra of operators $${\mathcal A}$$ acting in the linear space of polynomials, and an operator $$D_p\in {\mathcal A}$$ with $$D_p(p_n)=np_n$$ , we form a new sequence of polynomials $$(q_n)_n$$ by considering a linear combination of $$m+1$$ consecutive $$p_n$$ : $$q_n=p_n+\sum _{j=1}^m\beta _{n,j}p_{n-j}$$ . Using the concept of $$\mathcal {D}$$ -operator, we determine the structure of the sequences $$\beta _{n,j}, j=1,\ldots ,m,$$ so that the polynomials $$(q_n)_n$$ are eigenfunctions of an operator in the algebra $${\mathcal A}$$ . As an application, from the classical discrete families of Charlier, Meixner, and Krawtchouk, we construct orthogonal polynomials $$(q_n)_n$$ which are also eigenfunctions of higher-order difference operators. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01764276
- Volume :
- 41
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Constructive Approximation
- Publication Type :
- Academic Journal
- Accession number :
- 100275398
- Full Text :
- https://doi.org/10.1007/s00365-014-9251-5