𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Some properties of Bernoulli polynomials and their generalizations

✍ Scribed by Da-Qian Lu


Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
220 KB
Volume
24
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis


In this work, we investigate some well-known and new properties of the Bernoulli polynomials and their generalizations by using quasi-monomial, lowering operator and operational methods. Some of these general results can indeed be suitably specialized in order to deduce the corresponding properties and relationships involving the (generalized) Bernoulli polynomials.


📜 SIMILAR VOLUMES


Degenerate Bernoulli polynomials, genera
✍ Paul Thomas Young 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 204 KB

We prove a general symmetric identity involving the degenerate Bernoulli polynomials and sums of generalized falling factorials, which unifies several known identities for Bernoulli and degenerate Bernoulli numbers and polynomials. We use this identity to describe some combinatorial relations betwee

Arithmetic Properties of Bernoulli–Padé
✍ Karl Dilcher; Louise Louise 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 126 KB

A class of generating functions based on the Padé 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

Some results on the Apostol–Bernoulli an
✍ Weiping Wang; Cangzhi Jia; Tianming Wang 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 270 KB

The main object of this paper is to investigate the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials. We first establish two relationships between the generalized Apostol-Bernoulli and Apostol-Euler polynomials. It can be found that many results obtained before are special cases of th