Certain Finite Sums Pertaining to Leibnitz, Harmonic and Other Special Numbers

Year 2022, Volume: 9 Issue: 3, 187 - 198, 30.09.2022

Neslıhan Kılar

https://doi.org/10.54287/gujsa.1134534

Abstract

The present manuscript deals with some certain finite sums and identities pertaining to some special numbers. Using generating functions methods, some relations and identities involving the Apostol type Euler and combinatorial numbers, and also the Fubini type numbers and polynomials, are given. Then, by using some certain classes of special finite sums involving the following rational sum which is defined by Simsek (2021b): y(r,ϑ)=∑_(b=0)^r▒〖(-1)^r/((1+b) ϑ^(b+1) 〖(ϑ-1)〗^(r-b+1) ),〗many new certain finite sums and formulas related to the Leibnitz, Harmonic, Changhee, and Daehee numbers are obtained. Moreover, some applications of these results are presented.

Keywords

Leibnitz Numbers, Harmonic Numbers, Fubini Type Numbers, Changhee and Daehee Numbers

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