A class of generating functions based on the PadΓ© approximants of the exponential function gives a doubly infinite class of number and polynomial sequences. These generalize the Bernoulli numbers and polynomials, as well as other sequences found in the literature. We derive analogues of the Kummer c
Bernoulli Numbers and Polynomials via Residues
β Scribed by I-Chiau Huang; Su-Yun Huang
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 139 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0022-314X
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β¦ Synopsis
An algebraic theory of residues is used to evaluate summations of the form
Various identities involving Bernoulli numbers and polynomials are derived.
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.
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
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