Porubský, Štefan Identities involving covering systems. II. (English) Zbl 0821.11008 Math. Slovaca 44, No. 5, 555-568 (1994). This paper is a continuation of the author’s previous paper [Math. Slovaca 44, 153-162 (1994; Zbl 0809.11012)]. Here he proves further theorems illustrating the relation between some properties of covering systems and the validity of some identities involving Bernoulli and Euler numbers and polynomials. Reviewer: T.Šalát (Bratislava) Cited in 1 ReviewCited in 1 Document MSC: 11B68 Bernoulli and Euler numbers and polynomials 11A07 Congruences; primitive roots; residue systems Keywords:Bernoulli numbers; Bernoulli polynomials; Euler polynomials; covering systems; identities; Euler numbers Citations:Zbl 0809.11012 PDF BibTeX XML Cite \textit{Š. Porubský}, Math. Slovaca 44, No. 5, 555--568 (1994; Zbl 0821.11008) Full Text: EuDML OpenURL References: [1] BEEBEE J.: Bernoulli numbers and exact covering systems. Amer. Math. Monthly 99 (1992), 946-948. · Zbl 0776.11008 [2] CHOI S. L. G.: Covering the set of integers by congruences of distinct moduli. Math. Comp. 25 (1971), 885-895. · Zbl 0231.10004 [3] DEEBA E. Y.-RODRIGUES D. M.: Stirling’s series and Bernoulli numbers. Amer. Math. Monthly 98 (1991), 423-426. · Zbl 0743.11012 [4] LEHMER D. H.: A new approach to Bernoulli polynomials. Amer. Math. Monthly 95 (1988), 905-911. · Zbl 0663.10009 [5] MORIKAWA R.: On a method to construct covering systems. Bull. Fac. Liberal Arts Nagasaki Univ. 22 (1981), 1-11. · Zbl 0462.10002 [6] MORIKAWA R.: Some examples of covering sets. Bull. Fac. Liberal Arts Nagasaki Univ. 21 (1981), 1-4. · Zbl 0462.10003 [7] MORDELL L. J.: Integral formulae of arithmetical character. J. London Math. Soc. 33 (1958), 371-375. · Zbl 0081.27404 [8] NIELSEN N.: Traite elementaire des nombres de Bernoulli. Gauthier-Villars, Paris, 1923. [9] PORUBSKÝ Š.: Covering systems and generating functions. Acta Arith. 26 (1975), 223-231. · Zbl 0268.10044 [10] PORUBSKÝ, Š: On m times covering systems of congruences. Acta Arith. 29 (1976), 159-169. [11] PORUBSKÝ, Š: Identities involving covering systems I. Math. Slovaca 44 (1994), 153-162. · Zbl 0809.11012 [12] RAABE J. L.: Die Jacob Bernoulli’sche Function. Zurich, 1848. [13] RAABE J. L.: Mathematische Mitteilungen. Vol. I; II. Verlag von Meyer & Zeller, Zurich, 1857; 1858. [14] SAALSCHUTZ L.: Vorlesungen uber die Bernoullischen Zahlen. Verlag von Julius Springer, Berlin, 1893. [15] SCHINZEL A.: Reducibility of polynomials and covering systems of congruences. Acta Arith. 13 (1967), 91-101. · Zbl 0171.00701 [16] ZNÁM Š.: Vector-covering systems of arithmetical sequences. Czechoslovak Math. J. 24(99) (1974), 455-461. · Zbl 0311.10003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.