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Generalized Geometric Polynomials Via Steffensen’s Generalized Factorials and Tanny’s Operators

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Abstract

Our purpose is to give a generalization of geometric polynomials by applying an appropriate linear transformation on the generalized factorial function. Some identities are investigated including explicit formula, generating function and recurrence relations. Furthermore, some relations with other polynomials are given.

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References

  1. H. Belbachir and I.-E. Bousbaa, Translated Whitney and r-Whitney numbers: A combinatorial approach, Journal of Integer Sequences, 16(2) (2013), 3.

    MathSciNet  MATH  Google Scholar 

  2. K. N. Boyadzhiev, A series transformation formula and related polynomials, International Journal of Mathematics and Mathematical Sciences, 2005(23) (2005), 3849–3866.

    Article  MathSciNet  Google Scholar 

  3. K. N. Boyadzhiev and A. Dil, Geometric polynomials: Properties and applications to series with zeta values, Analysis Mathematica, 42(3) (2016), 203–224.

    Article  MathSciNet  Google Scholar 

  4. L. Carlitz, Eulerian numbers and polynomials, Mathematics Magazine, 32(5) (1959), 247–260.

    Article  MathSciNet  Google Scholar 

  5. G.-S. Cheon and J.-H. Jung, r-Whitney numbers of Dowling lattices, Discrete Mathematics, 312(15) (2012), 2337–2348.

    Article  MathSciNet  Google Scholar 

  6. L. Comtet, Advanced Combinatorics: The art of finite and infinite expansions, Springer Science & Business Media, 2012.

  7. C. B. Corcino, R. B. Corcino, I. Mező, and J. L. Ramírez, Some polynomials associated with the r-Whitney numbes, Proceedings-Mathematical Sciences, 128(3) (2018), 27.

    Article  Google Scholar 

  8. T. Diagana and M. Hamadoun, Some new identities and congruences for Fubini numbers, Journal of Number Theory, 173 (2017), 547–569.

    Article  MathSciNet  Google Scholar 

  9. A. Dil and V. Kurt, Investigating geometric and exponential polynomials with Euler-Seidel matrices, Journal of Integer Sequences, 14(2) (2011), 3.

    MathSciNet  MATH  Google Scholar 

  10. A. Dil and V. Kurt, Polynomials related to harmonic numbers and evaluation of harmonic number series II, Applicable Analysis and Discrete Mathematics (2011), 212–229.

  11. O. A. Gross, Preferential arrangements, The American Mathematical Monthly, 69(1) (1962), 4–8.

    Article  MathSciNet  Google Scholar 

  12. L. C. Hsu and P. J.-S. Shiue, A unified approach to generalized Stirling numbers, Advances in Applied Mathematics, 20(3) (1998), 366–384.

    Article  MathSciNet  Google Scholar 

  13. C. Jordan, Calculus of Finite Differences, Chelsea Publishing Company, New York 1950.

    MATH  Google Scholar 

  14. L. Kargın, Some formulae for products of geometric polynomials with applications, Journal of Integer Sequences, 20(2) (2017) 3.

    MathSciNet  MATH  Google Scholar 

  15. L. Kargın and B. Çekim, Higher order generalized geometric polynomials, Turkish Journal of Mathematics, 42(3) (2018), 887–903.

    MathSciNet  MATH  Google Scholar 

  16. L. Kargın and R. B. Corcino, Generalization of Mellin derivative and its applications, Integral Transforms and Special Functions, 27(8) (2016), 620–631.

    Article  MathSciNet  Google Scholar 

  17. I. Mező, A new formula for the Bernoulli polynomials, Results in Mathematics, 58(3–4) (2010), 329–335.

    Article  MathSciNet  Google Scholar 

  18. I. Mező, Periodicity of the last digits of some combinatorial sequences, Journal of Integer Sequences, 17(2) (2014), 3.

    MathSciNet  MATH  Google Scholar 

  19. T. K. Petersen, Eulerian numbers, In Eulerian Numbers, pp. 3–18. Birkhuser, New York, NY, 2015.

    Book  Google Scholar 

  20. J. Riordan, Combinatorial identities, 1(8), New York: Wiley, 1968.

    MATH  Google Scholar 

  21. G-C. Rota, The number of partitions of a set, The American Mathematical Monthly, 71(5) (1964), 498–504.

    Article  MathSciNet  Google Scholar 

  22. Q. M. Luo and H. M. Srivastava, Some generalizations of the Apostol-Bernoulli and Apostol-Euler polynomials, Journal of Mathematical Analysis and Applications 308(1) (2005), 290–302.

    Article  MathSciNet  Google Scholar 

  23. J. F. Steffensen, On the definition of the central factorial, Journal of the Institute of Actuaries (1886–1994), 64(2) (1933), 165–168.

    Article  Google Scholar 

  24. S. Tanny, On some numbers related to the Bell numbers, Canadian Mathematical Bulletin, 17(5) (1975), 733.

    Article  MathSciNet  Google Scholar 

  25. H. S. Wilf, Generating functionology, Academic Press, New York 1990.

    Google Scholar 

  26. W. A. Whitworth, Choice and chance, Hafner Publishing Company, New York 1867.

    MATH  Google Scholar 

  27. D. Zeitlin, Remarks on A Formula for Preferential Arrangements, The American Mathematical Monthly, 70(2) (1963), 183–187.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgement

The authors are thankful to the anonymous referee for valuable comments and suggestions that improved the clarity of this manuscript.

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Authors and Affiliations

  1. Faculty of Mathematics, RECITS Laboratory, USTHB, BP 32, El Alia 16111, Bab Ezzouar, Algiers, Algeria

    Hacène Belbachir & Yahia Djemmada

Authors
  1. Hacène Belbachir
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  2. Yahia Djemmada
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Correspondence to Hacène Belbachir or Yahia Djemmada.

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Belbachir, H., Djemmada, Y. Generalized Geometric Polynomials Via Steffensen’s Generalized Factorials and Tanny’s Operators. Indian J Pure Appl Math 51, 1713–1727 (2020). https://doi.org/10.1007/s13226-020-0491-8

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  • DOI: https://doi.org/10.1007/s13226-020-0491-8

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