Zobrazeno 1 - 10
of 304
pro vyhledávání: '"ISMAIL, MOURAD E. H."'
In this paper, we study a class of orthogonal polynomials defined by a three-term recurrence relation with periodic coefficients. We derive explicit formulas for the generating function, the associated continued fraction, the orthogonality measure of
Externí odkaz:
http://arxiv.org/abs/2412.08166
Autor:
Ismail, Mourad E. H., Zhou, Keru
We use the Poisson kernel of the continuous $q$-Hermite polynomials to introduces families of integral operators, which are semigroups of linear operators. We describe the eigenvalues and eigenfunctions of one family of operators. The action of the s
Externí odkaz:
http://arxiv.org/abs/2311.00261
We study the behavior of the smallest possible constants $d(a,b)$ and $d_n$ in Hardy's inequalities $$ \int_a^b\left(\frac{1}{x}\int_a^xf(t)dt\right)^2\,dx\leq d(a,b)\,\int_a^b [f(x)]^2 dx $$ and $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big
Externí odkaz:
http://arxiv.org/abs/2306.08172
We study two families of orthogonal polynomials. The first is a finite family related to the Askey-Wilson polynomials but the orthogonality is on the real line. A limiting case of this family is an infinite system of orthogonal polynomials whose mome
Externí odkaz:
http://arxiv.org/abs/2205.05280
In this paper, we expand functions of specific $q$-exponential growth in terms of its even (odd) Askey- Wilson $q$-derivatives at $0$ and $\eta=(q^{1/4}+q^{-1/4})/2$. This expansion is a $q$-version of the celebrated Lidstone expansion theorem, where
Externí odkaz:
http://arxiv.org/abs/2109.02500
We introduce three one-parameter semigroups of operators and determine their spectra. Two of them are fractional integrals associated with the Askey-Wilson operator. We also study these families as families of positive linear approximation operators.
Externí odkaz:
http://arxiv.org/abs/2012.07549
Autor:
Ismail, Mourad E. H., Saad, Nasser
Publikováno v:
Journal of Mathematical Physics 61, 033501 (2020)
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical physics. The anal
Externí odkaz:
http://arxiv.org/abs/2003.06730
Autor:
Ismail, Mourad E. H., Saad, Nasser
Publikováno v:
Journal of Difference Equations and Applications, 2020
We introduce a finite difference and $q$-difference analogues of the Asymptotic Iteration Method of Ciftci, Hall, and Saad. We give necessary, and sufficient condition for the existence of a polynomial solution to a general linear second-order differ
Externí odkaz:
http://arxiv.org/abs/2003.06726
We study a continued fraction due to Ramanujan, that he recorded as Entry 12 in Chapter 16 of his second notebook. It is presented in Part III of Berndt's volumes on Ramanujan's notebooks. We give two alternate approaches to proving Ramanujan's Entry
Externí odkaz:
http://arxiv.org/abs/1908.03333