Two closed forms for the Bernoulli polynomials
arXiv:1506.02137 · doi:10.1016/j.jnt.2015.07.021
Abstract
In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.
7 pages
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Cited by in corpus (9)
- Two closed forms for the Bernoulli polynomials
- Closed formulas and determinantal expressions for higher-order Bernoulli and Euler polynomials in terms of Stirling numbers
- A determinantal expression and a recursive relation of the Delannoy numbers
- Two closed forms for the Apostol-Bernoulli polynomials
- Closed-form formulas, determinantal expressions, recursive relations, power series, and special values of several functions used in Clark--Ismail's two conjectures
- Partial solutions to several conjectures on completely monotonic degrees for remainders in asymptotic expansions of the digamma function
- Appell-Carlitz numbers
- Explicit expressions for the related numbers of higher order Appell polynomials
- Parametric kinds of generalized Apostol-Bernoulli polynomials and their properties