ASYMPTOTIC BEHAVIOR OF BERNOULLI-DUNKL AND EULER-DUNKL POLYNOMIALS AND THEIR ZEROS

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI（2021）

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摘要

Bernoulli-Dunkl and Euler-Dunkl polynomials have been recently introduced as an extension of Bernoulli and Euler polynomials to the Dunkl context. In this article we study the asymptotic behavior of them and prove their convergence to suitable Bessel functions, which are the functions analogous to sine and cosine in the Dunkl context. Finally, we analyze the behavior of the zeros of the Bernoulli-Dunkl and Euler-Dunkl polynomials.

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关键词

Appell-Dunkl sequences, Bernoulli-Dunkl polynomials, Euler-Dunkl polynomials, Fourier series, Fourier-Dunkl series, Bessel functions, asymptotic behavior, distribution of zeros

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