Ostrovska, SofiyaOstrovska, SofiyaMathematics2024-07-052024-07-05201180898-12211873-766810.1016/j.camwa.2010.11.0252-s2.0-78951472266https://doi.org/10.1016/j.camwa.2010.11.025https://hdl.handle.net/20.500.14411/1565The 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.eninfo:eu-repo/semantics/openAccessq-integersq-binomial theoremLupas q-analogue of the Bernstein operatorAnalytic functionMeromorphic functionArticleQ1613527532WOS:000287553200002