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Beta-type polynomials and their generating functions

Author

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  • Simsek, Yilmaz

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.

Suggested Citation

  • Simsek, Yilmaz, 2015. "Beta-type polynomials and their generating functions," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 172-182.
    • Handle: RePEc:eee:apmaco:v:254:y:2015:i:c:p:172-182
    DOI: 10.1016/j.amc.2014.12.118
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    Cited by:

    1. Mehar Chand & Hanaa Hachimi & Rekha Rani, 2018. "New Extension of Beta Function and Its Applications," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-25, December.
    2. Mariem Tounsi, 2020. "The Extended Matrix-Variate Beta Probability Distribution on Symmetric Matrices," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 647-676, June.

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