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Beta-type polynomials and their generating functions
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DOI：10.1016/j.amc.2014.12.118.png)
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摘要
En 中文
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. (C) 2014 Elsevier Inc. All rights reserved.
Keyword:
Bernstein basis functions
Generating function
Beta polynomials
Beta function and Gamma function
Laplace transform
Combinatorial identity
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IF:
3.4
论文数:
2.3W
被引数:
3.3W
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