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Classical and Quantum Orthogonal Polynomials in One Variable
- M. Ismail
- Mathematics
- 21 November 2005
Foreword Preface 1. Preliminaries 2. Orthogonal polynomials 3. Differential equations, Discriminants and electrostatics 4. Jacobi polynomials 5. Some inverse problems 6. Discrete orthogonal…
The zeros of basic Bessel functions, the functions Jv + ax(x), and associated orthogonal polynomials☆
- M. Ismail
- Mathematics
- 1 March 1982
Generalized orthogonality and continued fractions
Abstract The connection between continued fractions and orthogonality which is familiar for J -fractions and T -fractions is extended to what we call R -fractions of types I and II. These continued…
The Combinatorics of q-Hermite polynomials and the Askey - Wilson Integral
- M. Ismail, D. Stanton, G. Viennot
- MathematicsEur. J. Comb.
- 1 October 1987
A generalization of ultraspherical polynomials
Some old polynomials of L. J. Rogers are orthogonal. Their weight function is given. The connection coefficient problem, which Rogers solved by guessing the formula and proving it by induction, is…
An electrostatics model for zeros of general orthogonal polynomials
- M. Ismail
- Mathematics
- 1 April 2000
We prove that the zeros of general orthogonal polynomials, subject to certain integrability conditions on their weight functions determine the equilibrium position of movable n unit charges in an…
Diagonalization of Certain Integral Operators
Abstract We study integral representations of formal inverses of the differential operator and the Askey-Wilson divided difference operators in different polynomial bases. The eigenvalues are related…
The associated Askey-Wilson polynomials
- M. Ismail, Mizan Rahman
- Mathematics
- 1991
We derive some contiguous relations for very well-poised 8 7 series and use them to construct two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson…
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