Name
Abstract | ||
|---|---|---|
We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ(x), supported on the interval (a,b) and the other with respect to the measure |x−c|τ|x−d|γdμ(x), where c and d are outside (a,b). We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0<τ,γ≤1 or γ=0 and 0<τ≤2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey–Wilson ones. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jat.2013.07.007 | Journal of Approximation Theory |
Keywords | Field | DocType |
Orthogonal polynomials,Classical orthogonal polynomials,q-orthogonal polynomials,Zeros,Interlacing,Monotonicity | Wilson polynomials,Combinatorics,Classical orthogonal polynomials,Orthogonal polynomials,Mathematical analysis,Gegenbauer polynomials,Discrete orthogonal polynomials,Jacobi polynomials,Hahn polynomials,Askey–Wilson polynomials,Mathematics | Journal |
Volume | ISSN | Citations |
175 | 0021-9045 | 0 |
PageRank | References | Authors |
0.34 | 5 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dimitar Dimitrov | 1 | 376 | 49.21 |
| Mourad E. H. Ismail | 2 | 75 | 25.95 |
| Fernando R. Rafaeli | 3 | 15 | 4.03 |