2019
DOI: 10.2298/fil1910085s
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A class of big (p,q)-Appell polynomials and their associated difference equations

Abstract: In the present paper, we introduce and investigate the big (p, q)-Appell polynomials. We prove an equivalance theorem satisfied by the big (p, q)-Appell polynomials. As a special case of the big (p, q)-Appell polynomials, we present the corresponding equivalence theorem, recurrence relation and difference equation for the big q-Appell polynomials. We also present the equivalence theorem, recurrence relation and differential equation for the usual Appell polynomials. Moreover, for the big (p, q)-Bernoulli polyn… Show more

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Cited by 3 publications
(1 citation statement)
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“…As the authors have mentioned, this sequence of rational numbers "is a sequence that can be considered on the crossroad of positivity of trigonometric sums, stable behavior of some classes of holomorphic functions and a set of Appell polynomials in several hypercomplex variables" [6, p. 77]. Regarding the class of Appell polynomials and their generalizations, one can find in the literature some research of these polynomials from several points of view, see for example [4,5,7] and [25][26][27]. Recalling some combinatorial properties from Leopold Vietoris (1891Vietoris ( -2002 [33], some interesting generalizations can be seen in [24].…”
Section: Introductionmentioning
confidence: 99%
“…As the authors have mentioned, this sequence of rational numbers "is a sequence that can be considered on the crossroad of positivity of trigonometric sums, stable behavior of some classes of holomorphic functions and a set of Appell polynomials in several hypercomplex variables" [6, p. 77]. Regarding the class of Appell polynomials and their generalizations, one can find in the literature some research of these polynomials from several points of view, see for example [4,5,7] and [25][26][27]. Recalling some combinatorial properties from Leopold Vietoris (1891Vietoris ( -2002 [33], some interesting generalizations can be seen in [24].…”
Section: Introductionmentioning
confidence: 99%