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http://dx.doi.org/10.5666/KMJ.2016.56.2.329

Korobov Polynomials of the Fifth Kind and of the Sixth Kind  

Kim, Dae San (Department of Mathematics, Sogang University)
Kim, Taekyun (Department of Mathematics, Kwangwoon University)
Kwon, Hyuck In (Department of Mathematics, Kwangwoon University)
Mansour, Toufik (University of Haifa, Department of Mathematics)
Publication Information
Kyungpook Mathematical Journal / v.56, no.2, 2016 , pp. 329-342 More about this Journal
Abstract
Recently, Korobov polynomials have been received a lot of attention, which are discrete analogs of Bernoulli polynomials. In particular, these polynomials are used to derive some interpolation formulas of many variables and a discrete analog of the Euler summation formula. In this paper, we extend these family of polynomials to consider the Korobov polynomials of the fifth kind and of the sixth kind. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials.
Keywords
Bernoulli polynomials; Frobenius-Euler polynomials; Korobov polynomials; Umbral calculus;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 S. Araci and M. Acikgoz, A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials, Adv. Stud. Contemp. Math., 22(3)(2012), 399-406.
2 A. Bayad and T. Kim, Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials, Russ. J. Math. Phys., 18(2)(2011), 133-143.   DOI
3 L. Carlitz, A degenerate Staudt-Clausen theorem, Arch. Math., 7(1956), 28-33.   DOI
4 L. Carlitz, Degenerate Stirling, Bernoulii and Eulerian numbers, Utilitas Math., 15(1979) 51-88.
5 R. Dere and Y. Simsek, Applications of umbral algebra to some special polynomials, Adv. Stud. Contemp. Math., 22(2012), 433-438.
6 D. Ding and J. Yang, Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials, Adv. Stud. Contemp. Math., 20(1)(2010), 7-21.
7 G. Hetyei, Enumeration by kernel positions, Adv. in Appl. Math., 42(2009), 445-470.   DOI
8 D. S. Kim and T. Kim, On degenerate Bell numbers and polynomials, preprint.
9 D. S. Kim and T. Kim, Degenerate falling factorial polynomials, preprint.
10 D. S. Kim and T. Kim, Korobov polynomials of the third kind and of the fourth kind, preprint.
11 D. S. Kim and T. Kim, A note on poly-Bernoulli and higher-order poly-Bernoulli polynomials, Russ. J. Math. Phys., 22(2015), 26-33.   DOI
12 T. Kim, Identities involving Laguerre polynomials derived from umbral calculus, Russ. J. Math. Phys., 21(2014), 36-45.   DOI
13 T. Kim and T. Mansour, Umbral calculus associated with Frobenius-type Eulerian polynomials, Russ. J. Math. Phys., 21(2014), 484-493.   DOI
14 N. M. Korobov, On some properties of special polynomials, Proceedings of the IV International Conference \Modern Problems of Number Theory and its Applications" (Russian)(Tula, 2001), 1(2001), 40-49.
15 N. M. Korobov, Speical polynomials and their applications, in "Diophantine Approci-mations", Mathematical Notes (Russian), Vol. 2, Izd. Moskov. Univ., Moscow, 1996, 77-89.
16 D. V. Kruchinin and V. V. Kruchinin, Application of a composition of generating func-tions for obtaining explicit formulas of polynomials, J. Math. Anal. Appl., 404(2013), 161-171.   DOI
17 S. Roman, More on the umbral calculus, with emphasis on the q-umbral calculus, J. Math. Anal. Appl., 107(1985), 222-254.   DOI
18 S. Roman, The umbral calculus, Dover Publ. Inc., New York, 2005.
19 A. V. Ustinov, Korobov polynomials and umbral calculus, Chebyshevskii Sb., 4:8(2003), 137-152.