IDENTITIES RELATED TO THE STIRLING NUMBERS AND MODIFIED APOSTOL-TYPE NUMBERS ON UMBRAL CALCULUS

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Komatsu T., ŞİMŞEK Y.

MISKOLC MATHEMATICAL NOTES, vol.18, no.2, pp.905-916, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.18514/mmn.2017.1458
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.905-916
  • Keywords: Bernoulli numbers and polynomials, Euler numbers and polynomials, Genocchi Bernoulli numbers and polynomials, Stirling numbers, Umbral calculus, Umbral algebra, UNIFIED PRESENTATION, BERNOULLI, POLYNOMIALS, EULER, UNIFICATION, FAMILIES
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, by using umbral calculus and umbral algebra methods, we derive several interesting identities and relations related to the modified and unification of the Bernoulli, Euler and Genocchi polynomials and numbers and the generalized (beta-) Stirling numbers of the second kind. We also give some applications and remarks related to these numbers and polynomials.