Moscow Journal of Combinatorics and Number Theory

A new explicit formula for Bernoulli numbers involving the Euler number

Sumit Kumar Jha

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at msp.org/moscow.

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We derive a new explicit formula for Bernoulli numbers in terms of the Stirling numbers of the second kind and the Euler numbers. As a corollary of our result, we obtain an explicit formula for the even Euler numbers in terms of the Stirling numbers of the second kind.

Article information

Source
Mosc. J. Comb. Number Theory, Volume 8, Number 4 (2019), 385-387.

Dates
Received: 17 June 2019
Revised: 24 July 2019
Accepted: 8 August 2019
First available in Project Euclid: 29 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.moscow/1572314455

Digital Object Identifier
doi:10.2140/moscow.2019.8.389

Mathematical Reviews number (MathSciNet)
MR4026546

Zentralblatt MATH identifier
07126251

Subjects
Primary: 11B68: Bernoulli and Euler numbers and polynomials

Keywords
Bernoulli numbers Stirling numbers of the second kind Euler numbers polylogarithm function

Citation

Jha, Sumit Kumar. A new explicit formula for Bernoulli numbers involving the Euler number. Mosc. J. Comb. Number Theory 8 (2019), no. 4, 385--387. doi:10.2140/moscow.2019.8.389. https://projecteuclid.org/euclid.moscow/1572314455


Export citation

References

  • Y. A. Brychkov, O. I. Marichev, and N. V. Savischenko, Handbook of Mellin transforms, CRC Press, Boca Raton, FL, 2019.
  • H. W. Gould, “Explicit formulas for Bernoulli numbers”, Amer. Math. Monthly 79 (1972), 44–51.
  • S. K. Jha, “Two new explicit formulas for the Bernoulli numbers”, preprint, 2019.
  • S. E. Landsburg, “Stirling numbers and polylogarithms”, unpublished note, 2009, http://www.landsburg.com/query.pdf.
  • E. W. Weisstein, “Bernoulli polynomial”, http://mathworld.wolfram.com/BernoulliPolynomial.html. From MathWorld.