A Note on Orthogonal Polynomials

Note on Certain Orthogonal Polynomials

A Note on Some Random Orthogonal Polynomials on a Compact Interval

We consider a uniform distribution on the set Mk of moments of order k ∈ N corresponding to probability measures on the interval [0, 1]. To each (random) vector of moments in M2n−1 we consider the corresponding uniquely determined monic (random) orthogonal polynomial of degree n and study the asymptotic properties of its roots if n → ∞.

On Orthogonal Matrix Polynomials

In this paper we deal with orthogonal matrix polynomials. First of all, we establish some basic notations and results we need later. A matrix polynomial P is a matrix whose entries are polynomials, or, equivalently, a combination P(t) = A 0 +A 1 t+ +A n t n , where A 0 ; ; A n are numerical matrices (the size of all the matrices which appear in this paper is N N). A positive deenite matrix of m...

A Note on Boole Polynomials

Boole polynomials play an important role in the area of number theory, algebra and umbral calculus. In this paper, we investigate some properties of Boole polynomials and consider Witt-type formulas for the Boole numbers and polynomials. Finally, we derive some new identities of those poly-nomials from the Witt-type formulas which are related to Euler polynomials.

A Note on Noncommutative Polynomials

1. Introduction. We shall say that an integral domain1 R satisfies condition (M) if any two nonzero elements of R have a nonzero common right multiple. In this note it is proved that if 5 is an extension of a ring R such that S is, roughly speaking, a noncommutative polynomial ring in one variable with R as a coefficient ring, and if R has the property (M), then 5 has property (M). In case R is...