Related papers: On bicomplex Pell and Pell-Lucas numbers
This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.
In this paper, we consstruct a new extended q-Bernoulli numbers and poly nomials. From these numbers, we derive the multiple zeta functions and give some relations between multiple Bernoulli numbers and multiple zeta functions.
We give new identities for some symmetric polynomials. As applications of these identities, we obtain some formulas for a higher order analogue of Fibonacci and Lucas numbers.
We use the inversion of coefficient arrays to define dual polynomials to the Fibonacci and Catalan-Fibonacci polynomials, and we explore the properties of these new polynomials sequences. Many of the arrays involved are Riordan arrays.…
This paper explores idempotent and nilpotent operators in bicomplex spaces, focusing on their properties and behavior. We define idempotent and nilpotent matrices in this framework and derive related results. Several theorems are presented…
In this note we give a survey about polynomials whose moments are multiples of super Catalan numbers and explore two different kinds of q-analogues.
The Super-Catalan numbers are a generalization of the Catalan numbers defined as $T(m,n) = \frac{(2m)!(2n)!}{2m!n!(m+n)!}$. It is an open problem to find a combinatorial interpretation for $T(m,n)$. We resolve this for $m=3,4$ using a…
The moments of the Lucas polynomials and of the Chebyshev polynomials of the first kind are (multiples of) central binomial coefficients and the moments of the Fibonacci polynomials and of the Chebyshev polynomials of the second kind are…
In this paper, we provide new applications of Fibonacci and Lucas numbers. In some circumstances, we find algebraic structures on some sets defined with these numbers, we generalize Fibonacci and Lucas numbers by using an arbitrary binary…
The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate hyperharmonic numbers, hyperharmonic numbers and degenerate harmonic numbers. In particular, we derive an explicit expression…
In this paper, we give some properties of the Tribonacci and Tribonacci-Lucas quaternions and obtain some identities for them.
Recently, Komastu introduced the concept of poly-Cauchy numbers and polynomials which generalize Cauchy numbers and polynomials. In this paper, we introduce new generaliza- tion of poly-Cauchy and poly-Bernoulli numbers and polynomials.…
This note presents some results about Hankel determinants of backwards shifted Catalan-like numbers and related sequences.
I study Hankel determinants of a class of sequences which can be interpreted as generalizations of the Catalan numbers and the central binomial coefficients. They follow a modular pattern with a frequent appearance of zeroes, so that the…
In this paper we consider combinatorial numbers $C_{m, k}$ for $m\ge 1$ and $k\ge 0$ which unifies the entries of the Catalan triangles $ B_{n, k}$ and $ A_{n, k}$ for appropriate values of parameters $m$ and $k$, i.e., $B_{n,…
In this paper, we introduce a generalization of Balancing and Balancing-Lucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties.
We will study the historical pathway of the emergence of Tessarines or Bicomplex numbers, from their origin as "imaginary" solutions of irrational equations, to their insertion in the context of study of the algebras of hypercomplex…
Given two infinite sequences with known binomial transforms, we compute the binomial transform of the product sequence. Various identities are obtained and numerous examples are given involving sequences of special numbers: Harmonic…
We reprove a few results concerning paperfolding sequences using properties of Catalan numbers modulo 2.
We present numerous interesting, mostly new, results involving the $n$-step Fibonacci numbers and $n$-step Lucas numbers and a generalization. Properties considered include recurrence relations, summation identities, including binomial and…