Abstract
In this paper, the author considers the twisted Catalan numbers and the twisted Catalan-Daehee numbers, which are arisen from p-adic fermionic integrals and p-adic invariant integrals, respectively. We give some explicit identities and properties for those twisted numbers and polynomials by using p-adic integrals or generating functions.
Highlights
The Catalan numbers were first introduced by the Mongolian mathematician Ming
Catalan-Daehee numbers and polynomials were introduced in [6] and considered the family of linear differential equations arising from the generating function of those numbers in order to derive some explicit identities involving Catalan-Daehee numbers and Catalan numbers
In [7], several properties and identities associated with Catalan-Daehee numbers and polynomials were derived by utilizing umbral calculus techniques
Summary
Antu in 1730, even though they were named after the French-Belgian mathematician Eugène. In [2], Dolgy et al represented Catalan numbers by the fermionic p-adic integral on Z p as follows:. Using (8), the authors defined the Catalan-Daehee numbers by the generating function n. Catalan-Daehee numbers and polynomials were introduced in [6] and considered the family of linear differential equations arising from the generating function of those numbers in order to derive some explicit identities involving Catalan-Daehee numbers and Catalan numbers. In [7], several properties and identities associated with Catalan-Daehee numbers and polynomials were derived by utilizing umbral calculus techniques. Dolgy et al gave some new identities for those numbers and polynomials derived from p-adic Volkenborn integrals on Z p in [1]. Several twisted numbers and polynomials are treated in the literatures (see [12,13,14])
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