On Miki's identity for Bernoulli numbers
โ Scribed by Ira M. Gessel
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 163 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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
Let {B.(x)} be the well-known Bernoulli polynemials. It is the purpose of this paper to determine pB~p-t~+b(x)modp ", where p is a prime, k, b nonnegative integers and x a rational p-integer. It is interesting to investigate arithmetic properties of {B,} and {Bn(x)}. For the work on this line one ma