On a Class of Polynomials with Integer Coefficients

2008/04/12 by Milan Janjić, Milan Janjic, Janjic, Milan
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #math.CV

paper · pdf · doi:10.48550/arxiv.0804.2018

arxiv created 2008/04/12 · openalex publication_date 2008/04/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A class P_n,m,p(x) of polynomials is defined. The combinatorial meaning of its coefficients is given. Chebyshev polynomials are the special cases of P_n,m,p(x). It is first shown that P_n,m,p(x) may be expressed in terms of P_n,0,p(x). From this we derive that P_n,2,2(x) may be obtain in terms of trigonometric functions, from which we obtain some of its important properties. Some questions about orthogonality are also concerned. Furthermore, it is shown that P_n,2,2(x) fulfills the same three terms recurrence as Chebyshev polynomials. Some others recurrences for P_n,m,p(x) and its coefficients are also obtained. At the end a formula for coefficients of Chebyshev polynomials of the second kind is derived.

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