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A NEW FAMILY OF FUBINI TYPE NUMBERS AND POLYNOMIALS ASSOCIATED WITH APOSTOL-BERNOULLI NUMBERS AND POLYNOMIALS

Yilmaz Simsek|Neslihan Kilar
대한수학회 (The Korean Mathematical Society)|2017.09|대한수학회지 (Journal of the KMS)|제54권 제5호|pp. 1605-1621

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참고문헌

키워드

Bernoulli numbersbinomial coefficientsStirling numbersFrobenius-Euler numbersgenerating functionsFubini numbersApostol-Bernoulli polynomialsfunctional equationsApostol-Bernoulli numberscombinatorial sum
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초록

The purpose of this paper is to construct a new family of the special numbers which are related to the Fubini type numbers and the other well-known special numbers such as the Apostol-Bernoulli numbers, the Frobenius-Euler numbers and the Stirling numbers. We investigate some fundamental properties of these numbers and polynomials. By using generating functions and their functional equations, we derive various formulas and relations related to these numbers and polynomials. In order to compute the values of these numbers and polynomials, we give their recurrence relations. We give combinatorial sums including the Fubini type numbers and the others. Moreover, we give remarks and observation on these numbers and polynomials.

Abstract

The purpose of this paper is to construct a new family of the special numbers which are related to the Fubini type numbers and the other well-known special numbers such as the Apostol-Bernoulli numbers, the Frobenius-Euler numbers and the Stirling numbers. We investigate some fundamental properties of these numbers and polynomials. By using generating functions and their functional equations, we derive various formulas and relations related to these numbers and polynomials. In order to compute the values of these numbers and polynomials, we give their recurrence relations. We give combinatorial sums including the Fubini type numbers and the others. Moreover, we give remarks and observation on these numbers and polynomials.

참고문헌 (34)

  1. M. Alkan, "Generating function for q-Eulerian polynomials and their decomposition and applications", Fixed Point Theory Appl, 2013(72), pp.14~ (2013)
  2. T. Apostol, "On the Lerch zeta function", Pacific J. Math, 1(2), pp.161~167 (1951)
  3. A. Bayad, "Some array type polynomials associated with special numbers and polynomials", Appl. Math. Comput, 244, pp.149~157 (2014)
  4. H. Belbachir, "Sums involving moments of reciprocals of binomial coefficients", J. Integer Seq, 14(6), pp.16~ (2011)
  5. M. Bona, "Introduction to Enumerative Combinatorics" (2007), The McGraw-Hill Companies, Inc
  6. N. P. Cakic, "On generalized Stirling numbers and polynomials", Math. Balkanica, 18(3-4), pp.241~248 (2004)
  7. L. Carlitz, "Eulerian numbers and polynomials", Math. Mag, 32, pp.247~260 (1959)
  8. C. A. Charalambides, "Ennumerative Combinatorics", pp.2002, Chapman&Hall
  9. J. Cigler, "Fibonacci polynomials and central factorial numbers", ~
  10. L. Comtet, "Advanced Combinatorics: The Art of Finite and Infinite Expansions" (1974), D. Rei-del Publishing Company
  11. G. B. Djordjevic, "Special classes of polynomials" (2014), University of Nis, Faculty of Technology Leskovac
  12. I. J. Good, "The number of ordering of n candidates when ties are permitted", Fibonacci Quart, 13, pp.11~18 (1975)
  13. S. Hu, "Two closed forms for the Apostol-Bernoulli polynomials", arXiv:1509.04190, ~
  14. T. Kim, "Identities involving Frobenius-Euler polynomials arising from non-linear dif-ferential equations", J. Number Theory, 132(12), pp.2854~2865 (2012)
  15. T. Kim, "New q-Euler numbers and polynomials associated with p-adic q-integrals", Advanced Studies in Contemporary Mathematics, 15(2), pp.243~252 (2007), 장전수학회
  16. 김태균, "On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions", 대한수학회지, 45(2), pp.435~453 (2008), 대한수학회
  17. Q. M. Luo, "Some relationships between the Apostol-Bernoulli and Apostol-Euler Polynomials", Comput. Math. Appl, 51(3-4), pp.631~642 (2006)
  18. Q. M. Luo, "Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind", Appl. Math. Comput, 217(12), pp.5702~5728 (2011)
  19. M. Muresan, "A Concrete Approach to Classical Analysis" (2009), Springer Science Business Media, LLC, Canadian Mathematical Society
  20. H. Ozden, "Unification of generating function of the Bernoulli, Euler and Genocchi numbers and polynomials", Amer. Inst. Phys. Conf. Proc, 1281, pp.1125~1128 (2010)
  21. H. Ozden, "Unified presentation of p-adic L-functions associated with unification of the special numbers", Acta Math. Hungar, 144(2), pp.515~529 (2014)
  22. H. Ozden, "Modification and unification of the apostol-type numbers and polynomials and their applications", Appl. Math. Comput, 235, pp.338~351 (2014)
  23. H. Ozden, "A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials", Comput. Math. Appl, 60(10), pp.2779~2787 (2010)
  24. V. M. Petrogradsky, "Witt’s formula for restricted Lie algebras", Adv. Appl. Math, 30, pp.219~227 (2003)
  25. Y. Simsek, "q-analogue of the twisted l-series and q-twisted Euler numbers", J. Number Theory, 100(2), pp.267~278 (2005)
  26. Y. Simsek, "Generating functions for generalized Stirling type numbers, Array type polyno-mials, Eulerian type polynomials and their applications", Fixed Point Theory A, 2013(87), pp.28~ (2013)
  27. Y. Simsek, "An explicit formula for the multiple Frobenius-Euler numbers and polynomials", J. Algebra Number Theory Appl, 4(3), pp.519~529 (2004)
  28. Y. Simsek, "A family of p-adic twisted interpolation functions associated with the modified Bernoulli numbers", Appl. Math. Comput, 216(10), pp.2976~2987 (2010)
  29. Y. Simsek, "On interpolation functions of the twisted generalized Frobenius-Euler numbers", Advanced Studies in Contemporary Mathematics, 15(2), pp.187~194 (2007), 장전수학회
  30. H. M. Srivastava, "Series Associated with the Zeta and Related Functions" (2001), Kluwer Academic Publishers
  31. H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier Science Publishers
  32. H.M. Srivastava, "A Treatise on Generating Functions" (1984), Ellis Horwood Limited Publisher
  33. H. M. Srivastava, "A unified presentation of certain meromorphic functions related to the families of the partial zeta type functions and the L-functions", Appl. Math. Comput, 219(8), pp.3903~3913 (2012)
  34. H. Tsumura, "On a p-adic interpolation of generalized Euler numbers and its applica-tions", Tokyo J. Math, 10(2), pp.281~293 (1987)

관련 논문AI추천

A note on -Fubini polynomialsMEHMET ACIKGOZ, SERKAN ARACI, UGUR DURAN장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제2호REMARKS ON RECURRENCE FORMULAS FOR THE APOSTOL-TYPE NUMBERS AND POLYNOMIALSIREM KUCUKOGLU, YILMAZ SIMSEK장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제4호COMBINATORIAL SUMS INVOLVING FUBINI TYPE NUMBERS AND OTHER SPECIAL NUMBERS AND POLYNOMIALS: APPROACH TRIGONOMETRIC FUNCTIONS AND P-ADIC INTEGRALSNESLIHAN KILAR, YILMAZ SIMSEK장전수학회 · Advanced Studies in Contemporary Mathematics2021 · 제31권 제1호Identities and relations on the $q$-Apostol type Frobenius-Euler numbers and polynomialsIrem Kucukoglu, Yilmaz Simsek대한수학회 · 대한수학회지2019 · 제56권 제1호Two variable higher-order Fubini polynomials권혁인, 김대산, 김태균, 박진우대한수학회 · 대한수학회지2018 · 제55권 제4호Apostol type Daehee numbers and polynomialsYilmaz Simsek장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호

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