Results 41 to 50 of about 120 (102)

A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1. We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a ...
Hasan Gökbaş, Mohammad W. Alomari
wiley   +1 more source

Fully degenerate Bell polynomials associated with degenerate Poisson random variables

Open Mathematics, 2021
Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al.
Kim Hye Kyung
doaj   +1 more source

The log-convexity of the poly-Cauchy numbers

, 2017
In 2013, Komatsu introduced the poly-Cauchy numbers, which generalizeCauchy numbers. Several generalizations of poly-Cauchy numbers have been con-sidered since then. One particular type of generalizations is that of multiparameter-poly-Cauchy numbers. In
Komatsu, Takao, Zhao, Feng-Zhen, Feng-Zhen Zhao, Takao Komatsu   +3 more
core   +1 more source

On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis

Open Mathematics, 2021
In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras.
Bajorska-Harapińska Beata, Ludew Jakub Jan, Smoleń-Duda Barbara, Wituła Roman   +3 more
doaj   +1 more source

Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants [PDF]

, 2012
MSC 2010: 11B83, 05A19, 33C45This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the ...
Savic, Natasa, Rajkovic, Predrag M., Barry, Paul   +2 more
core  

A closed formula for the generating function of p-Bernoulli numbers

, 2018
In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers in terms of harmonic numbers. As consequences of this generating function, we derive closed formulas for the nite summation of Bernoulli and harmonic ...
Rahmani, Mourad, Kargin, Levent, Levent Kargin, Mourad Rahmani   +3 more
core   +1 more source

Evaluation of integrals with hypergeometric and logarithmic functions

Open Mathematics, 2018
We provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions.
Sofo Anthony
doaj   +1 more source

Exact ranges of certain generalized polynomials with rational parameters

Annals of the West University of Timisoara: Mathematics and Computer Science
For fα(n)=⌊α2n⌋−⌊α⌊αn⌋⌋,   n∈ℕ,f_\alpha(n) = \lfloor \alpha^2 n \rfloor - \lfloor \alpha \lfloor \alpha n \rfloor \rfloor, \quad n \in \mathbb{N}, we give an exact finite description of Range(fα) for every positive rational parameter α.
Bényi Árpád, Ćurgus Branko
doaj   +1 more source

Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences

Open Mathematics
The Piatetski-Shapiro sequences are sequences of the form (⌊nc⌋)n=1∞{\left(\lfloor {n}^{c}\rfloor )}_{n=1}^{\infty } and the Beatty sequence is the sequence of integers (⌊αn+β⌋)n=1∞{(\lfloor \alpha n+\beta \rfloor )}_{n=1}^{\infty }.
Qi Jinyun, Guo Victor Zhenyu
doaj   +1 more source

On Cauchy Products of q−Central Delannoy Numbers

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023
In this study, we have examined q− central Delannoy numbers and their Cauchy products. We have given some related equalities using the properties of recurrence relations.
Halıcı Serpil
doaj   +1 more source