Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Analysis

International mathematical journal of analysis and its applications

Editor-in-Chief: Schulz, Friedmar

4 Issues per year


Cite Score 2016: 0.65

SCImago Journal Rank (SJR) 2016: 0.125
Source Normalized Impact per Paper (SNIP) 2016: 3.360

Mathematical Citation Quotient (MCQ) 2016: 0.34

Online
ISSN
2196-6753
See all formats and pricing
More options …
Volume 34, Issue 3

Issues

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

Feng Qi
  • School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, P. R. China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Bai-Ni Guo
  • School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, P. R. China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-08-01 | DOI: https://doi.org/10.1515/anly-2014-0003

Abstract.

This is a corrected version of http://dx.doi.org/10.1515/anly-2012-1238. 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.

Keywords: Alternative proof; explicit formula; Bernoulli number; Stirling number of the second kind; Faá di Bruno formula; Bell polynomial

MSC: 11B68; 11B73

We thank Professor Doron Zeilberger for drawing our attention to the books [Graham, Knuth and Patashnik, Concrete Mathematics. A Foundation for Computer Science, Addison-Wesley, Reading, 1989] and [Graham, Knuth and Patashnik, Concrete Mathematics. A Foundation for Computer Science, 2nd ed., Addison-Wesley, Amsterdam, 1994] and sketching the third proof in an e-mail on October 10, 2013. Thanks to his advice, we could find that the formula (1.2) originated from [Logan, Polynomials related to the Stirling numbers, AT&T Bell Laboratories Internal Technical Memorandum, August 10, 1987] and was listed as an incidental consequence of an answer to an exercise in page 536 in [Graham, Knuth and Patashnik, Concrete Mathematics. A Foundation for Computer Science, Addison-Wesley, Reading, 1989] and page 560 in [Graham, Knuth and Patashnik, Concrete Mathematics. A Foundation for Computer Science, 2nd ed., Addison-Wesley, Amsterdam, 1994].

About the article

Received: 2013-12-10

Accepted: 2014-01-14

Published Online: 2014-08-01

Published in Print: 2014-08-01


Citation Information: Analysis, Volume 34, Issue 3, Pages 311–317, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1515/anly-2014-0003.

Export Citation

© 2014 by De Gruyter. Copyright Clearance Center

Comments (0)

Please log in or register to comment.
Log in