Identities involving Bernoulli and Euler polynomials

• Type: Article in International Scientific Journal
• Date: 2018

Authors

Alzer, H (Author) Other; Yakubovich, SB (Author) FCUP

Journal

Title: Integral Transforms and Special Functions

Vol. 29

Pages: 43-61

ISSN: 1065-2469

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 0 Citations

Other information

Authenticus ID: P-00N-BYR

DOI: 10.1080/10652469.2017.1403437

Abstract (EN): We present various identities involving the classical Bernoulli and Euler polynomials. Among others, we prove that [ Sigma n/ 4] k= 0 (- 1) k Sigma n 4k Sigma Bn- 4k( z) 26k = 1 2n+ 1 Sigma n k= 0 (- 1) k 1 + ik ( 1 + i) k Sigma n k Sigma Bn- k( 2z) and Sigma n k= 1 22k- 1 Sigma 2n 2k - 1 Sigma B2k- 1( z) = Sigma n k= 1 k22k Sigma 2n 2k Sigma E2k- 1( z). Applications of our results lead to formulae for Bernoulli and Euler numbers, like, for instance, nEn- 1 = [ Sigma n/ 2] k= 1 22k - 1 k ( 22k - 2n) Sigma n 2k - 1 Sigma B2kBn- 2k.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19