SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2013 / Cilt: 42 - Sayı: 4

A Recurrence Relation for Bernoulli Numbers

Omer KUCUKSAKALLI
Pages
319–329
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This recurrence relation has an interesting connection with real cyclotomic fields.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Inspired by a result of Saalsch¨utz, we prove a recurrence relation forBernoulli numbers.
📊
Key Findings & Data:Inspired by a result of Saalsch¨utz, we prove a recurrence relation forBernoulli numbers.
💡
Conclusion & Impact:This recurrence relation has an interesting connection with real cyclotomic fields.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bernoulli numbers · cyclotomic fields · Newton’s identities.

Abstract

Inspired by a result of Saalsch¨utz, we prove a recurrence relation forBernoulli numbers. This recurrence relation has an interesting connection with real cyclotomic fields.

Özet

-

🔖

Cite This Article

KUCUKSAKALLI, O. (2022). A Recurrence Relation for Bernoulli Numbers. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 4, 319–329. https://ajindex.com/articles/530424

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (9)

  1. Agoh, T. and Dilcher, K. Shortened recurrence relations for Bernoulli numbers, Discrete Math. 309(4), 887–898, 2009.
  2. Apostol, T. M. An elementary view of Euler’s summation formula, Amer. Math. Monthly 106 (5), 409–418, 1999.
  3. Bromwich, T. J. I’A. An Introduction to the Theory of Infinite Series. Second edition. London, Macmillan; New York, St. Martin’s Press, 1965.
  4. Cox, D., Little, J. and O’Shea, D. Ideals, varieties, and algorithms. Second edition. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 1997.
  5. Gould, H. W. Explicit formulas for Bernoulli numbers, Amer. Math. Monthly 79, 44–51, 197 Harvey, D. A multimodular algorithm for computing Bernoulli numbers, Math. Comp. 79 (272), 2361–2370, 2010.
  6. Ireland, K. and Rosen, M. A Classical Introduction to Modern Number Theory. Second edition. Graduate Texts in Mathematics, 84. Springer-Verlag, New York, 1990.
  7. Kummer, E. E. Allgemeiner Beweis des Fermat’schen Satzes, dass die Gleichung x λ + y λ = z λ durch ganze Zahlenunl¨ osbar ist, f¨ ur alle diejenigen Potenz-Exponenten λ, welche ungerade Primzahlen sind und in den Z¨ ahlern der ersten (λ − 3)/2 Bernoulli’schen Zahlen als Factoren nicht vorkommen, J. Reine Angew. Math. 40, 131–138, 1850. Mills, S. The independent derivations by Leonhard Euler and Colin Maclaurin of the EulerMaclaurin summation formula, Arch. Hist. Exact Sci. 33 (1-3), 1–13, 1985. Saalsch¨ utz, L. Neue Formeln f¨ ur die Bernoullischen Zahlen, J. Reine Angew. Math. 126, 99–101, 1903.
  8. Sloane, N.J.A. On-Line Encyclopedia of Integer Sequences, http://www.oeis.org.
  9. Washington, L. C. Introduction to cyclotomic fields. Second edition. Graduate Texts in Mathematics, 83. Springer-Verlag, New York, 1997.