𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Padé approximation and Apostol–Bernoulli and Apostol–Euler polynomials

✍ Scribed by Marc Prévost

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
714 KB
Volume
233
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

Using the Padé approximation of the exponential function, we obtain recurrence relations between Apostol-Bernoulli and between Apostol-Euler polynomials. As applications, we derive some new lacunary recurrence relations for Bernoulli and Euler polynomials with gap of length 4 and lacunary relations for Bernoulli and Euler numbers with gap of length 6.

📜 SIMILAR VOLUMES

Some results on the Apostol–Bernoulli an
Some results on the Apostol–Bernoulli and Apostol–Euler polynomials
✍ 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

Arithmetic Properties of Bernoulli–Padé
Arithmetic Properties of Bernoulli–Padé Numbers and Polynomials
✍ 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

A note on the Bernoulli and Euler polyno
A note on the Bernoulli and Euler polynomials
✍ Gi-Sang Cheon 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 150 KB

In this paper, we obtain a simple property of the Bernoulli polynomials Bn(x) and the Euler polynomials Er~(X). As a consequence, the relationship between two polynomials is obtained from n k=0 ,~1