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- W2012380786 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." @default.
- W2012380786 created "2016-06-24" @default.
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- W2012380786 date "2015-03-01" @default.
- W2012380786 modified "2023-09-25" @default.
- W2012380786 title "Beta-type polynomials and their generating functions" @default.
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- W2012380786 doi "https://doi.org/10.1016/j.amc.2014.12.118" @default.
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