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Publications Influence

Some Fractional q -Integrals and q -Derivatives

- W. A. Al-Salam
- Mathematics
- 1 December 1966

A q -analogue of the integral ∣ f(t)dt is defined by means of which is an inverse of the q –derivative The present author ( 2 ) has recently obtained a q –nalogue of a formula of Cauchy, namely,… Expand

236 23

Characterization Theorems for Orthogonal Polynomials

- W. A. Al-Salam
- Mathematics
- 1990

We survey in this paper characterization theorems dealing with polynomial sets which are orthogonal on the real line.

170 19

ORTHOGONAL POLYNOMIALS ASSOCIATED WITH THE ROGERS-RAMANUJAN CONTINUED FRACTION

- W. A. Al-Salam, M. Ismail
- Mathematics
- 1 February 1983

We characterize the symmetric orthogonal polynomials {Pn(x)} such that {Pn(qnx)} is also orthogonal. This leads to orthogonal polynomials related to the denominator polynomials of the continued… Expand

53 5- PDF

$q$-beta integrals and the $q$-Hermite polynomials.

- W. A. Al-Salam, M. Ismail
- Mathematics
- 1 December 1988

42 5- PDF

Polynomials orthogonal with respect to discrete convolution

- W. A. Al-Salam, M. Ismail
- Mathematics
- 1 July 1976

Abstract The concept of “Discrete Convolution Orthogonality” is introduced and investigated. This leads to new orthogonality relations for the Charlier and Meixner polynomials. This in turn leads to… Expand

10 2

Some determinants of Bernoulli, Euler and related numbers

- W. A. Al-Salam, L. Carlitz
- Mathematics
- 1959

16 2

A $q$-beta integral on the unit circle and some biorthogonal rational functions

- W. A. Al-Salam, M. Ismail
- Mathematics
- 1 February 1994

In this paper we first consider a pair of polynomial sets which are biorthogonal on the unit circle with respect to a complex weight function. We then show how the biorthogonality of this pair of… Expand

25 2- PDF

A $q$-analog of a formula of Toscano.

- W. A. Al-Salam, L. Carlitz
- Mathematics
- 1957

8 1

Reproducing kernels for $q$-Jacobi polynomials

- W. A. Al-Salam, M. Ismail
- Mathematics
- 1977

We derive a family of reproducing kernels for the q-Jacobi polynomials 4(n"J)(X) = 241(q-f, q -l+f3; qa; q, qx). This is achieved by proving that the polynomials 4'fl)(x) satisfy a discrete Fredholm… Expand

7 1

Remarks on some operational formulas

- W. A. Al-Salam
- Mathematics
- 1965

L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’accord avec les conditions générales d’utilisation… Expand

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