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Some Fractional q -Integrals and q -Derivatives
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
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Characterization Theorems for Orthogonal Polynomials
We survey in this paper characterization theorems dealing with polynomial sets which are orthogonal on the real line.
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ORTHOGONAL POLYNOMIALS ASSOCIATED WITH THE ROGERS-RAMANUJAN CONTINUED FRACTION
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 continuedExpand
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Polynomials orthogonal with respect to discrete convolution
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 toExpand
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A $q$-beta integral on the unit circle and some biorthogonal rational functions
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 ofExpand
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A $q$-analog of a formula of Toscano.
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Reproducing kernels for $q$-Jacobi polynomials
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 FredholmExpand
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Remarks on some operational formulas
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’utilisationExpand
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