2 APPROACHES TO THE ASYMPTOTICS OF THE ZEROS OF A CLASS OF HYPERGEOMETRIC-TYPE POLYNOMIALS

Authors
MARTINES A SARSO A YANES R
Citation
A. Martines et al., 2 APPROACHES TO THE ASYMPTOTICS OF THE ZEROS OF A CLASS OF HYPERGEOMETRIC-TYPE POLYNOMIALS, Sbornik. Mathematics, 83(2), 1995, pp. 483-494
Citations number
21
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Sbornik. Mathematics → ACNP
ISSN journal
10645616
Volume
83
Issue
2
Year of publication
1995
Pages
483 - 494
Database
ISI
SICI code
1064-5616(1995)83:2<483:2ATTAO>2.0.ZU;2-7
Abstract
A class of hypergeometric-type differential equations is considered. I t is shown that its polynomial solutions y(n) exhibit an orthogonality with respect to a ''varying measure'' (a sequence of measures) on R. From this relation the asymptotic distribution of zeros is obtained by means of a potential theory approach. Moreover, the WKB or semiclassi cal approximation is used to construct an asymptotically exact sequenc e of absolutely continuous measures that approximate the zero distribu tion of y(n).