Recurrences for the derivative polynomials for tangent and secant

2022/06/15 by Guo-Niu Han, Han, Guo-Niu, Shi-Mei Ma +1
Mathematics · Physics and Astronomy · #05A05 #33B10 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2206.07590

openalex publication_date 2022/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we choose the derivative polynomials for tangent and secant as basis sets of polynomial space. From this viewpoint, we first give an expansion of the derivative polynomials for tangent in terms of the derivative polynomials for secant, and we then present a result in the reverse direction. We also discuss the relationships between alternating derivative polynomials and Eulerian polynomials. As applications, we give certain expansions of the alternating derivative polynomials, which indicate that the alternating derivative polynomials share more properties with the Chebyshev polynomials.

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