Name
Abstract | ||
|---|---|---|
We introduce operators of q-fractional integration through inverses of the Askey-Wilson operator and use them to introduce a q-fractional calculus. We establish the semigroup property for fractional integrals and fractional derivatives. We study properties of the kernel of q-fractional integral and show how they give rise to a q-analogue of Bernoulli polynomials, which are now polynomials of two variables, x and y. As q->1 the polynomials become polynomials in x-y, a convolution kernel in one variable. We also evaluate explicitly a related kernel of a right inverse of the Askey-Wilson operator on an L^2 space weighted by the weight function of the Askey-Wilson polynomials. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1006/jath.2001.3644 | Journal of Approximation Theory |
Keywords | Field | DocType |
q-fourier series,q-bernoulli polynomials,continuous q -ultraspherical polynomials,askey-wilson polynomials,q-fractional calculus,inverse of an askey-wilson operator,q-lommel polynomials | Inverse,Bernoulli polynomials,Mathematical analysis,Pure mathematics,Askey–Wilson polynomials,Operator (computer programming),Semigroup,Mathematics | Journal |
Volume | Issue | ISSN |
114 | 2 | 0021-9045 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mourad E. H. Ismail | 1 | 75 | 25.95 |
| Mizan Rahman | 2 | 2 | 1.51 |