Let [x] be the integral part of x. Let p > 5 be a prime. In the paper we mainly determine ) in terms of Euler and Bernoulli numbers. For example, we have where E n is the nth Euler number and B n is the nth Bernoulli number.
Arithmetic Identities Involving Bernoulli and Euler Numbers
β Scribed by Wenchang Chu; Chenying Wang
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 328 KB
- Volume
- 55
- Category
- Article
- ISSN
- 1422-6383
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this paper we prove some identities involving Bernoulli and Stirling numbers, relation for two or three consecutive Bernoulli numbers, and various representations of Bernoulli numbers.
Let B m be the mth Bernoulli number in the even suffix notation and let q(a, n)=(a j(n) -1)/n be the Fermat-Euler quotient, where a, n \ 2 are relatively prime positive integers and j is the Euler totient function. The main purpose of this paper is to devise a certain congruence involving the Bernou
We use properties of p-adic integrals and measures to obtain congruences for higher-order Bernoulli and Euler numbers and polynomials, as well as for certain generalizations and for Stirling numbers of the second kind. These congruences are analogues and generalizations of the usual Kummer congruenc
We extend Euler's well-known quadratic recurrence relation for Bernoulli numbers, which can be written in symbolic notation as (B 0 + B 0 ) n = -nB n-1 -(n -1)B n , to obtain explicit expressions for (B k + B m ) n with arbitrary fixed integers k, m 0. The proof uses convolution identities for Stirl