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Generating Functions for the Fubini Type Polynomials and Their Applications

In: Exploring Mathematical Analysis, Approximation Theory, and Optimization

Author

Listed:
  • Yilmaz Simsek

    (University of Akdeniz)

  • Neslihan Kilar

    (Niğde Ömer Halisdemir University)

Abstract

One of the aims of this chapter is to give Fubini type numbers and polynomials discovered with the help of generating functions or defined by combinatorial methods and also their general properties with known methods or techniques that we have found. The second purpose of this chapter is to give formulas and relations that we have just found, besides the known ones, using generating functions and their functional equations. The third purpose of this chapter is to give the relations between Fubini-type numbers and polynomials and other special numbers and polynomials. The fourth of the purposes of this chapter will be to give tables with Fubini-type numbers and polynomials, as well as other special numbers and special polynomials. In addition, by using Wolfram Mathematica version 12.0, graphs of Fubini type polynomials and their generating functions, surface graphs and mathematical codes will be given. The fifth purpose of this chapter, some known applications in the theory of approximation with Fubini-type numbers and polynomials are summarized. The sixth of the purposes of this chapter is to give zeta-type functions that interpolate Fubini-type numbers and polynomials at negative integers. Moreover, throughout this chapter, we are tried diligently to present the results obtained in comparison with other known results and their reductions, taking into account the relevant sources.

Suggested Citation

  • Yilmaz Simsek & Neslihan Kilar, 2023. "Generating Functions for the Fubini Type Polynomials and Their Applications," Springer Optimization and Its Applications, in: Nicholas J. Daras & Michael Th. Rassias & Nikolaos B. Zographopoulos (ed.), Exploring Mathematical Analysis, Approximation Theory, and Optimization, pages 279-380, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-46487-4_15
    DOI: 10.1007/978-3-031-46487-4_15
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