On the Lupas <i>q</i>-transform

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Date

2011

Authors

Ostrovska, Sofiya

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Pergamon-elsevier Science Ltd

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Mathematics
(2000)
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Abstract

The Lupas q-transform emerges in the study of the limit q-Lupas operator. The latter comes out naturally as a limit for a sequence of the Lupas q-analogues of the Bernstein operator. Lately, it has been studied by several authors from different perspectives in mathematical analysis and approximation theory. This operator is closely related to the q-deformed Poisson probability distribution, which is used widely in the q-boson operator calculus. (Lambda(q)f)(z) := 1/(-z; q)(infinity) . Sigma(infinity)(k=0) f(1 - q(k))q(k(k-1)/2)/(q; q)(k) z(k). In this paper, we study some analytic properties of (Lambda(q)f)(z). In particular, we examine the conditions under which Lambda(q)f can either be an entire function, or a rational one. (C) 2010 Elsevier Ltd. All rights reserved.

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Keywords

q-integers, q-binomial theorem, Lupas q-analogue of the Bernstein operator, Analytic function, Meromorphic function

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8

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Volume

61

Issue

3

Start Page

527

End Page

532

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