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

---

DAĞLI M. C., CAN M.

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

• 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
• Open Archive Collection: AVESIS Open Access Collection
• 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.