Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure Articles uri icon

publication date

  • January 2016

start page

  • 732

end page

  • 746

issue

  • 1

volume

  • 433

International Standard Serial Number (ISSN)

  • 0022-247X

Electronic International Standard Serial Number (EISSN)

  • 1096-0813

abstract

  • This paper deals with monic orthogonal polynomials generated by a Geronimus canonical spectral transformation of the Laguerre classical measure, i.e., 1/x - cx(alpha)e(-x)dx + N delta(x - c) for x is an element of [0, infinity), alpha > -1, a free parameter N is an element of R+ and a shift c < 0. We analyze the asymptotic behavior (both strong and relative to classical Laguerre polynomials) of these orthogonal polynomials as n tends to infinity.

keywords

  • orthogonal polynomials; canonical spectral trans formations of measures; asymptotic analysis; hypergeometric func tions