Related papers: Convolution identities for Tetranacci numbers
Many kinds of convolution identities have been considered about several numbers, including Bernoulli, Euler, Genocchi, Cauchy, Stirling, and Fibonacci numbers. The well-known basic result about Bernoulli numbers is due to Euler. The…
Convolutions for Tribonacci numbers involving binomial coefficients are treated with ordinary generating functions and the diagonalization method of Hautus and Klarner. In this way, the relevant generating function can be established, which…
We present various identities in the form of convolutions involving Stirling numbers of both kinds, Lah numbers, and binomial coefficients. Certain convolution polynomials are discussed also. The proofs are based on several series…
Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…
We derive some Fibonacci and Lucas identities which contain inverse binomial coefficients. Extension of the results to the general Horadam sequence is possible, in some cases.
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.
This paper considers the properties of Tribonacci numbers on identities, matrices, and determinants. In the first front part, we obtain several symmetric identities of Tribonacci numbers by a matrix-based approach and binomial inversion…
In this paper, we give some interesting and new identities of q-Bernoulli numbers which are derived from convolutions on the ring of p-adic integers.
We give a general multiplication-convolution identity for the multivariate and bivariate rank generating polynomial of a matroid. The bivariate rank generating polynomial is transformable to and from the Tutte polynomial by simple algebraic…
By applying the derivative operators to Chu-Vandermonde convolution, several general harmonic number identities are established.
In this note, we present several identities involving binomial coefficients and the two kind of Stirling numbers.
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
We obtain closed form expressions for convolutions of scale transformations within a certain subset of Appell polynomials. This subset contains the Bernoulli, Apostol-Euler, and Cauchy polynomials, as well as various kinds of their…
We introduce the degenerate Bernoulli numbers of the second kind as a degenerate version of the Bernoulli numbers of the second kind. We derive a family of nonlinear differential equations satisfied by a function closely related to the…
By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…
New convolution identities of hypergeometric Bernoulli polynomials are presented. Two different approaches to proving these identities are discussed, corresponding to the two equivalent definitions of hypergeometric Bernoulli polynomials as…
In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.
In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a…
We combinatorially prove Tetranacci, Tetranacci-Fibonacci, and additional identities using only squares and dominoes on a hexagonal double-strip. Some of these are new proofs of old identities, and others we believe have never been seen…