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COMBINATORIAL SUMS INVOLVING FUBINI TYPE NUMBERS AND OTHER SPECIAL NUMBERS AND POLYNOMIALS: APPROACH TRIGONOMETRIC FUNCTIONS AND P-ADIC INTEGRALS

NESLIHAN KILAR|YILMAZ SIMSEK
장전수학회 (Jangjeon Mathematical Society)|2021.01|Advanced Studies in Contemporary Mathematics|제31권 제1호|pp. 75-87

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참고문헌

키워드

Euler numbers and polynomialsDaehee numbersp-adic integralsGenerating functionsStirling numbersnoulli numbers and polynomialsChanghee numbersFubini type numbers and polynomialsTrigonometric functions
주제분류수학

초록

The aim of this paper is to obtain combinatorial sums, formulas and rela- tions by applications functional equations of generating functions for some well-known special numbers and polynomials, trigonometric functions and p-adic integrals. These combinatorial sums, formulas and relations are related to the Bernoulli numbers, the Euler numbers, the Daehee numbers, the Changhee numbers, the Stirling numbers, the Fubini type numbers and polynomials, two parametric kinds of Fubini-type poly- nomials, the central factorial numbers, and other special numbers and polynomials.

Abstract

The aim of this paper is to obtain combinatorial sums, formulas and rela- tions by applications functional equations of generating functions for some well-known special numbers and polynomials, trigonometric functions and p-adic integrals. These combinatorial sums, formulas and relations are related to the Bernoulli numbers, the Euler numbers, the Daehee numbers, the Changhee numbers, the Stirling numbers, the Fubini type numbers and polynomials, two parametric kinds of Fubini-type poly- nomials, the central factorial numbers, and other special numbers and polynomials.

참고문헌 (48)

  1. M. Abramowitz, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables" (1972), National Bureau of Standards, U.S. Dept. of Commerce
  2. M. Bona, "Introduction to Enumerative Combinatorics" (2007), The McGraw-Hill Companies, Inc.
  3. P. L. Butzer, "Central factorial numbers; their main properties and some applications", Numer. Funct. Anal. Optim, 10(5-6), pp.419~488 (1989)[DOI]
  4. L. Comtet, "Advanced Combinatorics" (1974), D. Reidel Publication Company
  5. "Fibonacci polynomials and central factorial numbers"[URL]
  6. E. Y. Deeba, "Bernoulli numbers and trigonometric functions", Int. J. Math. Educ. Sci. Technol, 21(2), pp.275~282 (1990)
  7. I. J. Good, "The number of ordering of n candidates when ties are permitted", Fibonacci Quart, 13, pp.11~18 (1975)
  8. N. Kilar, "Fubini Type Numbers and Their Generating Functions", MSc, pp.2017
  9. Neslihan Kilar, "A NEW FAMILY OF FUBINI TYPE NUMBERS AND POLYNOMIALS ASSOCIATED WITH APOSTOL-BERNOULLI NUMBERS AND POLYNOMIALS", 대한수학회지, 54(5), pp.1605~1621 (2017), 대한수학회
  10. N. Kilar, "Some relationships between Fubini type polynomials and other special numbers and polynomials", AIP Conference Proceedings, 2116(10017), pp.100017-1~100017-4 (2019)[DOI]
  11. N. Kilar, "Identities and relations for Fubini type numbers and polynomials via gener-ating functions and p-adic integral approach", Publ. Inst. Math. Nouv. Ser, 106(120), pp.113~123 (2019)
  12. NESLIHAN KILAR, "Relations on Bernoulli and Euler polynomials related to trigonometric functions", Advanced Studies in Contemporary Mathematics, 29(2), pp.191~198 (2019), 장전수학회
  13. N. Kilar, "Two parametric kinds of Eulerian-type polynomials associated with Euler's formula", Symmetry, 11, pp.1~19 (2019)
  14. N. Kilar, "Some classes of generating functions for generalized Hermite- and Chebyshev-type polynomials: Analysis of Euler's formula", arXiv:1907.03640v1, 1~31 (2019)
  15. N. Kilar, "A note on Hermite-based Milne Thomson type polynomials involving Cheby-shev polynomials and other polynomials", Techno-Science, 3, pp.8~14 (2020)
  16. Neslihan Kilar, "IDENTITIES FOR SPECIAL NUMBERS AND POLYNOMIALS INVOLVING FIBONACCI-TYPE POLYNOMIALS AND CHEBYSHEV POLYNOMIALS", Advanced Studies in Contemporary Mathematics, 30(4), pp.495~504 (2020), 장전수학회
  17. N. Kilar, "Identities and relations for Hermite-based Milne-Thomson polynomials associated with Fibonacci and Chebyshev polynomials", Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat. RACSAM, 115(28), pp.1~20 (2021)
  18. N. Kilar, "A special approach to derive new formulas for some special numbers and polynomials", Turk. J. Math, 44, pp.2217~2240 (2020)
  19. N. Kilar, "New computational formulas for special numbers and polynomials derived from applying trigonometric functions to generating functions", ~
  20. T. Kim, "q-Volkenborn integration", Russ. J. Math. Phys, 19, pp.288~299 (2002)
  21. T. Kim, "A note on q -Volkenborn integration", Proc. Jangjeon Math. Soc, 8(1), pp.13~17 (2005)
  22. T. Kim, "q-Euler numbers and polynomials associated with p-adic q-integral and basic q-zeta function", Trend Math. Inf. Cent. Math. Sci, 9, pp.7~12 (2006)
  23. T. Kim, "q-Euler numbers and polynomials associated with p-adic q-integrals", J. Nonlinear Math. Phys, 14(1), pp.15~27 (2007)
  24. T. Kim, "On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Zp at q = -1", J. Math. Anal. Appl, 331(2), pp.779~792 (2007)
  25. 김태균, "On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions", 대한수학회지, 45(2), pp.435~453 (2008), 대한수학회
  26. T. Kim, "A note on the q-integral and q-series", Adv. Stud. Contemp. Math, 2(1), pp.37~45 (2000)
  27. D. S. Kim, "Daehee numbers and polynomials", Appl. Math. Sci. Ruse, 7(120), pp.5969~5976 (2013)
  28. D. S. Kim, "A note on Changhee numbers and polynomials", Adv. Stud. Theor. Phys, 7, pp.993~1003 (2013)
  29. 김대산, "Two variable higher-order Fubini polynomials", 대한수학회지, 55(4), pp.975~986 (2018), 대한수학회
  30. T. Kim, "Two variable higher-order central Fubini polynomials", J. Inequal. Appl, 146, pp.1~13 (2019)
  31. T. Kim, "Symmetric identities for Fubini polynomials", Sym-metry, 10(6)통권 : 219, pp.1~7 (2018)
  32. T. Kim, "Some identities for Euler and Bernoulli polynomials and their zeros", Axioms, 7, pp.1~19 (2018)
  33. I. Kucukoglu, "An approach to negative hypergeometric distribution by generating function for special numbers and polynomials", Turk. J. Math, 43, pp.2337~2353 (2019)
  34. M. Masjed-Jamei, "Symbolic computation of some power-trigonometric series", J. Symb. Comput, 80, pp.273~284 (2017)
  35. M. Masjed-Jamei, "A new type of Euler polynomials and numbers", Mediterr. J. Math, 15(138), pp.1~17 (2018)
  36. M. Masjed-Jamei, "An extension of the Euler-Maclaurin quadrature formula using a parametric type of Bernoulli polynomials", Bull. Sci. Math, 156(102798), pp.1~26 (2019)
  37. E. D. Rainville, "Special Functions" (1960), The Macmillan Company
  38. W. H. Schikhof, "Ultrametric Calculus: An Introduction to p-adic Analysis, Cambridge Studies in Advanced Mathematics 4" (1984), Cambridge University Press
  39. Y. Simsek, "Special functions related to Dedekind-type DC-sums and their applications", Russ. J. Math. Phys, 17(4), pp.495~508 (2010)
  40. Y. Simsek, "Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications", Fixed Point Theory Appl, 87, pp.1~28 (2013)
  41. Y. Simsek, "Explicit formulas for p-adic integrals: Approach to p-adic distributions and some fam-ilies of special numbers and polynomials", Montes Taurus J. Pure Appl. Math, 1(1), pp.1~76 (2019)
  42. M. R. Spiegel, "Mathematical Handbook of Formulas and Tables" (1998), McGraw-Hill
  43. H. M. Srivastava, "Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials", Appl. Math. Inf. Sci, 5(3), pp.390~444 (2011)
  44. H. M. Srivastava, "A Parametric type of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials", Appl. Math. Inf. Sci, 12, pp.907~916 (2018)
  45. H. M. Srivastava, "Some new generalizations and applications of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials", Rocky Mt. J. Math, 49, pp.681~697 (2019)
  46. H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier Science Publishers
  47. H. M. Srivastava, "A parametric kind of the Fubini-type polynomials", Rev. R. Acad. Cienc. Exactas Fs. Nat., Ser. A Mat., (RACSAM), 113, pp.3253~3267 (2019)[DOI]
  48. D. Zwillinger, "CRC Standard Mathematical Tables (Advances in Applied Mathematics)" (2018), CRC Press, Taylor & Francis Group

관련 논문AI추천

Integral representations and formulas for the unified and modified presentation of Fubini numbers and polynomialsNeslihan Kilar장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2025 · 제28권 제1호A NEW FAMILY OF FUBINI TYPE NUMBERS AND POLYNOMIALS ASSOCIATED WITH APOSTOL-BERNOULLI NUMBERS AND POLYNOMIALSNeslihan Kilar, Yilmaz Simsek대한수학회 · 대한수학회지2017 · 제54권 제5호ON CENTRAL FUBINI POLYNOMIALS ASSOCIATED WITH CENTRAL FACTORIAL NUMBERS OF THE SECOND KIND권종겸, 김대산, 김태균장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제4호IDENTITIES ON THE CHANGHEE NUMBERS AND APOSTOL-TYPE DAEHEE POLYNOMIALSYILMAZ SIMSEK장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제2호A note on -Fubini polynomialsMEHMET ACIKGOZ, SERKAN ARACI, UGUR DURAN장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제2호Apostol type Daehee numbers and polynomialsYilmaz Simsek장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호

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