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1
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Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence

100%
Mező I., Dil A.
Open Mathematics
|
2009
|
tom 7
|
nr 2
310-321
EN
In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization of Gosper’s identity. A classification of second order recurrence sequences is also given with the help of this method.
2
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Fourier series of functions involving higher-order ordered Bell polynomials

61%
Kim T., Kim D. S., Jang G.-W., Jang L. C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1606-1617
EN
In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the preferred arrangement numbers). In this paper, we study Fourier series of functions related to higher-order ordered Bell polynomials and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.
3
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Differential equations associated with generalized Bell polynomials and their zeros

52%
Ryoo S. C.
Open Mathematics
|
2016
|
tom 14
|
nr 1
807-815
EN
In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.
4
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Fully degenerate poly-Bernoulli numbers and polynomials

52%
Kim T., Kim D. S., Seo J.-J.
Open Mathematics
|
2016
|
tom 14
|
nr 1
545-556
EN
In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.
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