Beta-type polynomials and their generating functions

Yilmaz Simsek

Applied Mathematics and Computation, 2015, vol. 254, issue C, 172-182

Abstract: We construct generating functions for beta-type rational functions and the beta polynomials. By using these generating functions, we derive a collection of functional equations and PDEs. By using these functional equations and PDEs, we give derivative formulas, a recurrence relation and a variety of identities related to these polynomials. We also give a relation between the beta-type rational functions and the Bernstein basis functions. Integrating these identities and relations, we derive various combinatorial sums involving binomial coefficients, some old and some new, for the beta-type rational functions and the Bernstein basis functions. Finally, by applying the Laplace transform to these generating functions, we obtain two series representations for the beta-type rational functions.

Keywords: Bernstein basis functions; Generating function; Beta polynomials; Beta function and Gamma function; Laplace transform; Combinatorial identity (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:254:y:2015:i:c:p:172-182

DOI: 10.1016/j.amc.2014.12.118

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