A class of polynomials and connections with Bernoulli’s numbers

Milovanovic G. V., ŞİMŞEK Y., Stojanovic V. S.

Journal of Analysis, cilt.27, sa.3, ss.709-726, 2019 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s41478-018-0116-3
  • Dergi Adı: Journal of Analysis
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.709-726
  • Anahtar Kelimeler: 11B68, 11B83, 26C05, 26C10, Algebraic polynomial, Bernoulli numbers, Generating function, Real zeros, Recurrence relation
  • Akdeniz Üniversitesi Adresli: Evet

Özet

© 2018, Forum D'Analystes, Chennai.Motivated by certain problems connected with the stochastic analysis of the recursively defined time series, in this paper, we define and study some polynomial sequences. Beside computation of these polynomials and their connection to the Euler–Apostol numbers, we prove some basic properties and give an interesting connection of these polynomials with the well-known Bernoulli numbers, as well as some new summation formulas for Bernoulli’s numbers. Finally, we prove that zeros of these polynomials are simple, real and symmetrically distributed in [0,1].