Related papers: k Sequences of Generalized Van der Laan and Genera…
In this paper, we shall find a new connection between $n$th degree polynomial mod $p$ congruence with $n$ roots and higher-order Fibonacci and Lucas sequences. We shall first discuss the recent work been done in sequences and their…
In this paper, we study a class of sequences of polynomials linked to the sequence of Bell polynomials. Some sequences of this class have applications on the theory of hyperbolic differential equations and other sequences generalize…
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.
The present paper deals with multiplication formulas for the Apostol-Genocchi polynomials of higher order and deduces some explicit recursive formulas. Some earlier results of Carlitz and Howard in terms of Genocchi numbers can be deduced.…
This paper analyzes the concept of orthogonality in second-order polynomial sequences that have Binet formula similar to that of the Fibonacci and Lucas numbers, referred to as Generalized Fibonacci Polynomials (GFP). We give a technique to…
Using general identities for difference operators, as well as a technique of symbolic computation and tools from probability theory, we derive very general kth order (k \ge 2) convolution identities for Bernoulli and Euler polynomials. This…
In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.
In this paper, generalized Pell graphs $\Pi _{n,k}$, $k\ge 2$, are introduced. The special case of $k=2$ are the Pell graphs $\Pi _{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are…
Sequences of Genocchi numbers of the first and second kind are considered. For these numbers, an approach based on their representation using sequences of polynomials is developed. Based on this approach, for these numbers some identities…
We explore new types of binomial sums with Fibonacci and Lucas numbers. The binomial coefficients under consideration are $\frac{n}{n+k}\binom{n+k}{n-k}$ and $\frac{k}{n+k}\binom{n+k}{n-k}$. The identities are derived by relating the…
Using elementary methods, we establish old and new relations between binomial coefficients, Fibonacci numbers, Lucas numbers, and more.
We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference…
This note gives an elementary exposition of a variant of the spread polynomials in terms of Fibonacci and Lucas polynomials.
In the present paper, we define the generalized Kwang-Wu Chen matrix. Basic properties of this generalization, such as explicit formulas and generating functions are presented. Moreover, we focus on a new class of generalized Fubini…
In this paper we give some interesting equation of p-adic q-integrals on Zp. From those p-adic q-integrals, we present a systemic study of some families of extended Carlitz q-Bernoulli numbers and polynomials in p-adic number field.
This paper is devoted to the study of eigen-sequences for some important operators acting on sequences. Using functional equations involving generating functions, we completely solve the problem of characterizing the fixed sequences for the…
The purpose of this paper is to derive some identities of the higher order generalized twisted Bernoulli numbers and polynomials attached to $\chi$ from the properties of the p-adic invariant integrals.
Let $(L_n^{(k)})_{n\geq 2-k}$ be the sequence of $k$-generalized Lucas numbers for some fixed integer $k\ge 2$, whose first $k$ terms are $0,\;\ldots\;,\;0,\;2,\;1$ and each term afterward is the sum of the preceding $k$ terms. In this…
We prove a linear recurrence relation for a large family of generalized Schreier sets, which generalizes the Fibonacci recurrence proved by Bird and higher order Fibonacci recurrence proved by the second author et al. Furthermore, we show a…
We study the value distribution of diagonal forms in k variables and degree d with random real coefficients and positive integer variables, normalized so that mean spacing is one. We show that the l-correlation of almost all such forms is…