Name
Abstract | ||
|---|---|---|
We give a general method of characterizing symmetric orthogonal polynomials through a certain type of connection relations. This method is applied to Al-Salam-Chihara, Askey-Wilson, and Meixner-Pollaczek polynomials. This characterization technique unifies and extends some previous characterization results of Lasser and Obermaier and Ismail and Obermaier. Along the way we explicitly evaluate the connection coefficients in the expansion of D"q^2p"n in terms of {p"k}, where D"q is the Askey-Wilson operator and {p"k} are general Askey-Wilson polynomials. As a limiting case we derive the corresponding connection coefficients in the expansion of W^2W"n in terms of {W"k}, where W is the Wilson operator and {W"k} are general Wilson polynomials. Using the connection relation for Askey-Wilson polynomials, we obtain a characterization for the two-parameter symmetric Askey-Wilson polynomials. The connection relations between D^mP"n^(^@a^,^@b^), D:=d/dx and {P"k^(^@a^,^@b^)} are also derived. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.aam.2012.04.004 | Advances in Applied Mathematics |
Keywords | Field | DocType |
askey-wilson polynomial,corresponding connection coefficient,orthogonal polynomial,previous characterization result,askey-wilson operator,general askey-wilson polynomial,connection relation,general wilson polynomial,characterization technique unifies,connection coefficient,general method,jacobi polynomials,recurrence relations,wilson polynomials | Wilson polynomials,Combinatorics,Orthogonal polynomials,Classical orthogonal polynomials,Mathematical analysis,Macdonald polynomials,Discrete orthogonal polynomials,Hahn polynomials,Askey–Wilson polynomials,Mathematics,Difference polynomials | Journal |
Volume | Issue | ISSN |
49 | 2 | 0196-8858 |
Citations | PageRank | References |
1 | 0.38 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mourad E. H. Ismail | 1 | 75 | 25.95 |
| Plamen Simeonov | 2 | 42 | 9.49 |