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math.NTJan 1, 2014
19
citations (OpenAlex)
authors
  • Bai-Ni Guo
  • Feng Qi
institutions
  • Henan Polytechnic University
arXiv abstractPDF
paper

Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers

arXiv:1401.4257 · doi:10.1515/anly-2014-0003

Abstract

In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.

6 pages

Cited by in corpus (11)

  • Two closed forms for the Bernoulli polynomials
  • Explicit expressions for a family of Bell polynomials and derivatives of some functions
  • Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function
  • An explicit formula for Bernoulli numbers in terms of Stirling numbers of the second kind
  • Diagonal recurrence relations, inequalities, and monotonicity related to Stirling numbers
  • An explicit formula for Bernoulli polynomials in terms of r-Stirling numbers of the second kind
  • An explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind
  • A new explicit formula for Bernoulli and Genocchi numbers in terms of Stirling numbers
  • Rapidly Convergent Summation Formulas involving Stirling Series
  • Sums of powers of integers and hyperharmonic numbers
  • Parametric kinds of generalized Apostol-Bernoulli polynomials and their properties
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