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Identities arising from higher-order Daehee polynomial bases

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Here we will derive formulas for expressing any polynomial as linear combinations of two kinds of higherorder Daehee polynomial basis. Then we will apply these formulas to certain polynomials in order to get new and interesting identities involving higher-order Daehee polynomials of the first kind and of the second kind.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-07-28
zaakceptowano
2015-01-02
online
2015-01-20
Twórcy
autor
  • Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea, dskim@sogang.ac.kr
autor
  • Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea, tkkim@kw.ac.kr
Bibliografia
  • [1] S. Araci and M. Acikgoz, A note on the Frobenius-euler numbers and polynomials associated with Bernstein polynomials, Adv. Stud. Contemp. Math. 22 (2012), no. 3, 399–406.
  • [2] A. Bayad and T. Kim, Identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials, Adv. Stud. Contemp. Math. 20 (2010), no. 2, 247–253.
  • [3] D. Ding and J. Yang, Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials, Adv. Stud. Contemp. Math. 20 (2010), no. 1, 7–21.
  • [4] G. V. Dunne and C. Schubert, Bernoulli number identities from quantum field theory and topological string theory, Commun. Number Theory Phys. 7 (2013), no. 2, 225–249.[WoS][Crossref]
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  • [6] S. Gaboury, R. Tremblay, and B.-J. Fugère, Some explicit formulas for certain new classes of Bernoulli, Euler and Genocchipolynomials, Proc. Jangjeon Math. Soc. 17 (2014), no. 1, 115–123.
  • [7] I. M. Gessel, On Miki’s identities for Bernoulli numbers, J. Number Theory 110 (2005), no. 1, 75–82.[WoS][Crossref]
  • [8] D. S. Kim and T. Kim, Bernoulli basis and the product of several Bernoulli polynomials, Int. J. Math. Math. Sci. Art. ID 463659(2012), 12 pp.
  • [9] , Daehee numbers and polynomials, Appl. Math. Sci. (Ruse) 7 (2013), no. 120, 5969–5976.
  • [10] , Some identities of Bernoulli and Euler polynomials arising from umbral calculus, Adv. Stud. Contemp. Math. 23 (2013),no. 1, 159–171.
  • [11] , Some identities of higher order Euler polynomials arising from Euler basis, Integral Transforms Spec. Funct. 24 (2013),no. 9, 734–738.[WoS]
  • [12] D. S. Kim, T. Kim, S.-H. Lee, and J.-J. Seo, Higher-order Daehee numbers and polynomials, Int. J. Math. Anal. (Ruse) 8 (2014),no. 6, 273–283.
  • [13] D. S. Kim, T. Kim, and J.-J. Seo, Higher-order Daehee polynomials of the first kind with umbral calculus, Adv. Stud. Contemp.Math. 24 (2014), no. 1, 5–18.
  • [14] T. Kim, An invariant p-adic integral associated with Daehee numbers, Integral Transforms Spec. Funct. 13 (2002), no. 1, 65–69.
  • [15] , Identities involving Laguerre polynomials derived from umbral calculus, Russ. J. Math. Phys. 21 (2014), no. 1, 36–45.[WoS]
  • [16] T. Kim, D. S. Kim, D. V. Dolgy, and S. H. Rim, Some identities on the Euler numbers arising from Euler basis polynomials, Ars.Combin. 109 (2013), 433–446.
  • [17] T. Kim and Y. Simsek, Analytic continuation of the multiple Daehee q-l-functions associated with Daehee numbers, Russ. J.Math. Phys. (2008).[WoS]
  • [18] A. Kudo, A congruence of generalized Bernoulli number for the character of the first kind, Adv. Stud. Contemp. Math. 2 (2000),1–8.[Crossref]
  • [19] Q.-M. Luo and F. Qi, Relationskind between generalied Bernoulli numbers and polynomials and generalized Euler numbers andpolynomials, Adv. Stud. Contemp. Math. 7 (2003), no. 1, 11–18.
  • [20] H. Miki, A relation between Bernoulli numbers, J. Number Theory 10 (1978), no. 3, 297–302.[Crossref]
  • [21] H. Ozden, I. N. Cangul, and Y. Simsek, Remarks on q-Bernoulli numbers associated with Daehee numbers, Adv. Stud. Contemp.Math. 18 (2009), no. 1, 41–48.
  • [22] S. Roman, The umbral calculus, Pure and Applied Mathematics, vol. 111, Academic Press, Inc. [Harcourt Brace Jovanovich,Publishers], New York, 1984. MR 741185 (87c:05015)
  • [23] E. Sen, Theorems on Apostol-Euler polynomials of higher order arising from Euler basis, Adv. Stud. Contemp. Math. 23 (2013),no. 2, 337–345.
  • [24] J.-J. Seo, S. H. Rim, T. Kim, and S. H. Lee, Sums products of generalized Daehee numbers, Proc. Jangjeon Math. Soc. 17(2014), no. 1, 1–9.
  • [25] K. Shiratani and S. Yokoyama, An application of p-adic convolutions, Mem. Fac. Sci. Kyushu Univ. Ser. A 36 (1982), no. 1, 73–83.
  • [26] Y. Simsek, S.-H. Rim, L.-C. Jang, D.-J. Kang, and J.-J. Seo, A note on q-Daehee sums, J. Anal. Comput. 1 (2005), no. 2, 151–160.
  • [27] Z. Zhang and H. Yang, Some closed formulas for generalized Bernoulli-Euler numbers and polynomials, Proc. Jangjeon Math.Soc. 11 (2008), no. 2, 191–198.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0019
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