Citation:
Journal of Approximation Theory, 2015, v. 196, pp. 111-130
ISSN:
0021-9045
DOI:
10.1016/j.jat.2015.03.005
Sponsor:
The authors thank the comments and suggestions made by the referees which helped improve
the manuscript. First author’s research was partially supported by FAPESP of Brazil, under
grant 2012/21042-0. First and second authors’ research was partially supported by Ministerio
de Economía y Competitividad of Spain, under grant MTM2012-36732-C03-01.
Let μ be a finite positive Borel measure supported on R , L[f]=xf′′+(α+1−x)f′ with α>−1 , or L[f]=12f′′−xf′ , and m a natural number. We study algebraic, analytic and asymptotic properties of the sequence of monic polynomials {Qn}n>m that satisfy thLet μ be a finite positive Borel measure supported on R , L[f]=xf′′+(α+1−x)f′ with α>−1 , or L[f]=12f′′−xf′ , and m a natural number. We study algebraic, analytic and asymptotic properties of the sequence of monic polynomials {Qn}n>m that satisfy the orthogonality relations
∫L[Qn](x)xkdμ(x)=0for all0≤k≤n−1.
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We also provide a fluid dynamics model for the zeros of these polynomials.[+][-]