.png){kind=icon}
Return
Beta-type polynomials and their generating functions
.png){kind=icon}
PRE
AI
DOI：10.1016/j.amc.2014.12.118.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
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.
Keywords:
Bernstein basis functions
Generating function
Beta polynomials
Beta function and Gamma function
Laplace transform
Combinatorial identity
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
3.4
Papers:
2.3W
Citations:
3.3W
Organization
No organization information available
Cited Papers
.png){kind=icon}
ShareSave
ShareSave