Certain identities, connection and explicit formulas for the Bernoulli, Euler numbers and Riemann zeta -values

2014/06/20 by Semyon Yakubovich, Yakubovich, Semyon
Mathematics · #11B68 #11B73 #11B83 #11M06 #12E10 #33C10 #44A15 #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #math.CA #msc:11B68 #msc:11B73 #msc:11B83 #msc:11M06 #msc:12E10 #msc:33C10 #msc:44A15

paper · pdf · doi:10.48550/arxiv.1406.5345

arxiv created 2014/06/20 · openalex publication_date 2014/06/20 · arxiv updated 2014/06/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Various new identities, recurrence relations, integral representations, connection and explicit formulas are established for the Bernoulli, Euler numbers and the values of Riemann's zeta function. To do this, we explore properties of some Sheffer's sequences of polynomials related to the Kontorovich-Lebedev transform.

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