ON THE INTEGRAL OF PRODUCTS OF HIGHER-ORDER BERNOULLI AND EULER POLYNOMIALS


Creative Commons License

DAĞLI M. C., CAN M.

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, vol.57, no.1, pp.7-20, 2017 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.7169/facm/1567
  • Journal Name: FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.7-20
  • Keywords: Bernoulli polynomials and numbers, Dedekind sums, integrals, recurrence relations, DEDEKIND SUMS
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, we derive a formula on the integral of products of the higher-order Euler polynomials. By the same method, similar relations are obtained for l higher-order Bernoulli polynomials and r higher-order Euler polynomials. Moreover, we establish a connection between these results and the generalized Dedekind sums and Hardy-Berndt sums.