Asymptotic behavior of varying discrete Jacobi-Sobolev orthogonal polynomials

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• 作者：Juan F. Mañ ; as-Mañ ; as^a ; ^{jmm939@ual.es" class="auth_mail" title="E-mail the corresponding author} ; Francisco Marcellá ; n^b ; ^{pacomarc@ing.uc3m.es" class="auth_mail" title="E-mail the corresponding author} ; Juan J. Moreno-Balcá ; zar^a ; ^c ; ^{balcazar@ual.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：33C47 ; 42C05
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：300
• 期：Complete
• 页码：341-353
• 全文大小：486 K

文摘

In this contribution we deal with a varying discrete Sobolev inner product involving the Jacobi weight. Our aim is to study the asymptotic properties of the corresponding orthogonal polynomials and the behavior of their zeros. We are interested in Mehler–Heine type formulae because they describe the essential differences from the point of view of the asymptotic behavior between these Sobolev orthogonal polynomials and the Jacobi ones. Moreover, this asymptotic behavior provides an approximation of the zeros of the Sobolev polynomials in terms of the zeros of other well-known special functions. We generalize some results appeared in the literature very recently.