An explicit formula for Bernoulli polynomials in terms of $r$-Stirling numbers of the second kind

Abstract

In the paper, the authors establish an explicit formula for computing Bernoulli polynomials at non-negative integer points in terms of $r$-Stirling numbers of the second kind.

4 pages

References in corpus (3)

• An explicit formula for computing Bell numbers in terms of Lah and Stirling numbers
• Alternative proofs of a formula for Bernoulli numbers in terms of Stirling numbers
• A new explicit formula for Bernoulli and Genocchi numbers in terms of Stirling numbers

Cited by in corpus (5)

• Two closed forms for the Bernoulli polynomials
• Explicit expressions for a family of Bell polynomials and derivatives of some functions
• An explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind
• An explicit Formula for Bernoulli Polynomials with a $q$ Parameter in Terms of $r$-Whitney Numbers
• A note on the coefficients of power sums of arithmetic progressions