Identities for the classical polynomials through sums of Liouville type. (English) Zbl 1291.11059
Polynomials defined recursively over the integers such as Dickson polynomials, Chebyshev polynomials, Fibonacci polynomials, Lucas polynomials, Bernoulli polynomials, Euler polynomials, and many others have been extensively studied in the past. Most of these polynomials have some type of relationship between them and share a large number of interesting properties. They have been also found to be topics of interest in many different areas of pure and applied sciences. Most recently, some of these families of polynomials have been found
to be useful in cryptography and related topics, which keep making them a very interesting area of research for many people in this era of communication. In this paper, we use a sum of Liouiville type to prove new properties concerning many of these families of polynomials.
MSC:
11B83 | Special sequences and polynomials |
11C08 | Polynomials in number theory |
11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
11B68 | Bernoulli and Euler numbers and polynomials |
11B75 | Other combinatorial number theory |