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Kim, T. et al. Degenerate Stirling Polynomials of the Second Kind and Some Applications. Symmetry, 2019, 11(8), 1046
Open AccessArticle

Some New Families of Special Polynomials and Numbers Associated with Finite Operators

Department of Mathematics, Faculty of Science, University of Akdeniz, Antalya TR-07058, Turkey
Symmetry 2020, 12(2), 237; https://doi.org/10.3390/sym12020237
Received: 26 December 2019 / Revised: 14 January 2020 / Accepted: 29 January 2020 / Published: 4 February 2020
The aim of this study was to define a new operator. This operator unify and modify many known operators, some of which were introduced by . Many properties of this operator are given. Using this operator, two new classes of special polynomials and numbers are defined. Many identities and relationships are derived, including these new numbers and polynomials, combinatorial sums, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Daehee numbers, and the Changhee numbers. By applying the derivative operator to these new polynomials, derivative formulas are found. Integral representations, including the Volkenborn integral, the fermionic p-adic integral, and the Riemann integral, are given for these new polynomials.
Keywords: generating function; bernoulli numbers; euler numbers; stirling numbers; central factorial numbers; daehee numbers; changhee numbers; special functions; operators, p-adic integral generating function; bernoulli numbers; euler numbers; stirling numbers; central factorial numbers; daehee numbers; changhee numbers; special functions; operators, p-adic integral
MDPI and ACS Style

Simsek, Y. Some New Families of Special Polynomials and Numbers Associated with Finite Operators. Symmetry 2020, 12, 237.

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