Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Orthogonal polynomials defined by a recurrence relation


Author: Paul G. Nevai
Journal: Trans. Amer. Math. Soc. 250 (1979), 369-384
MSC: Primary 42C05
MathSciNet review: 530062
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: R. Askey has conjectured that if a system of orthogonal polynomials is defined by the three term recurrence relation

$\displaystyle x{p_{n\, - \,1}}\left( x \right)\, = \,\frac{{{\gamma _{n\, - \,1... ...amma _{n\, - \,2}}}} {{{\gamma _{n\, - \,1}}}}\,{p_{n\, - \,2}}\left( x \right)$

and

$\displaystyle {\alpha _n}\, = \,\frac{{{{( - 1)}^n}}} {n}\,{\text{const}}\,{\text{ + }}O\left( {\frac{1} {{{n^2}}}} \right),$

$\displaystyle \frac{{{\gamma _n}}} {{{\gamma _{n + 1}}}}\, = \,\frac{1} {2}\, +... ...1)}^n}}} {n}\,{\text{const}}\,{\text{ + }}O\left( {\frac{1} {{{n^2}}}} \right),$

then the logarithm of the absolutely continuous portion of the corresponding weight function is integrable. The purpose of this paper is to prove R. Askey's conjecture and solve related problems.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42C05

Retrieve articles in all journals with MSC: 42C05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1979-0530062-6
Article copyright: © Copyright 1979 American Mathematical Society