Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지

A q-ANALOGUE OF $\omega-BERNOULLI$ NUMBERS AND THEIR APPLICATIONS

  • Published : 2001.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider that the q-analogue of w$\omega-Bernoulli numbers\; B_i(\omega, q)$. And we calculate the sums of products of two q-analogue of $\omega-Bernoulli numbers B_i(\omega, q)$ in complex cases. From this result, we obtain the Euler type formulas of the Carlitz´s q-Bernoulli numbers $\beta_i(q)$ and q-Bernoulli numbers $B_i(q)$. And we also calculate the p-adic Stirling type series by the definition of $B_i(\omega, q)$ in p-adic cases.

Keywords

References

  1. Duke Math. J. v.15 q-Bernoulli numbers and polynomials L. Carlitz
  2. London Math. Soc. Lecture Note series v.46 p-adic Analysis a Short Course on Recent work N. Koblitz
  3. Kyushu. J. Math. v.48 On explicit formulas of p-adic q-L-functions T. Kim
  4. Ref. Fac. Sci. Saga Univ. Math. v.22 An analogue of Bernoulli numbers and their congruences
  5. J. of Number Theory v.74 Sums of Procducts of Two q-Bernoulli Numbers J. Satoh
  6. Nagoya Math. J. v.127 A construction of q-analogue of Dedekind sums
  7. Comm. Korean. Math. Soc. v.14 On q-analogue of Stirling series J.-W.Son;D. S. Jang