Research article Special Issues

Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomials

  • Received: 23 December 2024 Revised: 14 February 2025 Accepted: 14 February 2025 Published: 20 February 2025
  • MSC : 05A19, 11B73, 11B83

  • By utilizing the generating function of higher-order Bernoulli polynomials, we uncover novel relationships that intertwine higher-order Bernoulli polynomials, higher-order Bernoulli numbers, Stirling numbers of the second kind, and central factorial numbers of the second kind. Leveraging these interconnections, we successfully rederive the identities formulated by Qi and Taylor, specifically those pertaining to Stirling numbers of the second kind and central factorial numbers of the second kind. Additionally, we derive series expansions for both positive integer and real powers of the sinc and sinhc functions.

    Citation: Aimin Xu. Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomials[J]. AIMS Mathematics, 2025, 10(2): 3197-3206. doi: 10.3934/math.2025148

    Related Papers:

  • By utilizing the generating function of higher-order Bernoulli polynomials, we uncover novel relationships that intertwine higher-order Bernoulli polynomials, higher-order Bernoulli numbers, Stirling numbers of the second kind, and central factorial numbers of the second kind. Leveraging these interconnections, we successfully rederive the identities formulated by Qi and Taylor, specifically those pertaining to Stirling numbers of the second kind and central factorial numbers of the second kind. Additionally, we derive series expansions for both positive integer and real powers of the sinc and sinhc functions.



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