Multiple orthogonal polynomials associated with the exponential integral

Multiple orthogonal polynomials associated with Macdonald functions

We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the Hermite-Padé table. We give some properties of these polynomials: differential properties, a Rodrigues type formula and explicit formulas for the third order linear recurrence relation. 1 Macdonald functions ...

Exact Bounds for Orthogonal Polynomials Associated with Exponential Weights*

Solving singular integral equations by using orthogonal polynomials

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

Symmetric Orthogonal Polynomials and the Associated Orthogonal L-polynomials

We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained. Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx2)(l x2)~1/2, k>0.

Multiple orthogonal polynomials

Results on multiple orthogonal polynomials will be surveyed. Multiple orthogonal polynomials are intimately related to Hermite–Pad e approximants and often they are also called Hermite–Pad e polynomials. Special attention will be paid to an application of multiple orthogonal polynomials and to analytic theory of two model families of general multiple orthogonal polynomials, referred to as Angel...