Related papers: Convolution identities for Tribonacci numbers via …

This paper studies a family of convolution quadratures, a numerical technique for efficient evaluation of convolution integrals. We employ the block generalized Adams method to discretize the underlying initial value problem, departing from…

In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of $\sinc$ functions. We then give a general formula to compute the integral on the real line of the…

The exponential generating function of ordinary generating functions of diagonal sequences of general Sheffer triangles is computed by an application of Lagrange's theorem. For the special Jabotinsky type this is already known. An analogous…

We study matrices which transform the sequence of Fibonacci or Lucas polynomials with even index to those with odd index and vice versa. They turn out to be intimately related to generalized Stirling numbers and to Bernoulli, Genocchi and…

Given an odd prime p, we present three independent ways of relating modulo p certain truncated convolutions of divided Bernoulli numbers to certain full convolutions of divided Bernoulli numbers.

Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given. By applying this generating function, not only derivative of these polynomials but also…

This paper presents an innovative approach to the study of recurrent sequences by introducing the concept of arithmetic pseudo-operators. Unlike conventional operators, these pseudo-operators are pure complex numbers with specific…

Using the methods of classical invariant theory a general approach to finding of identities for Bernulli, Euler and Hermite polynomials is proposed.

Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…

We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these…

The notion of 'bifurcating continued fractions' is introduced. Two coupled sequences of non-negative integers are obtained from an ordered pair of positive real numbers in a manner that generalizes the notion of continued fractions. These…

We consider Problem 6.94 posed in the book Concrete Mathematics by Graham, Knuth, and Patashnik, and solve it by using bivariate exponential generating functions. The family of recurrence relations considered in the problem contains many…

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra…

In this study, we introduce the generalized Tribonacci hyperbolic spinors and properties of this new special numbers system by the generalized Tribonacci numbers, which are one of the most general form of the third-order recurrence…

In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer…

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…

The operational calculus associated with Hermite numbers has been shown to be an effective tool for simplifying the study of special functions. Within this context, Hermite polynomials have been viewed as Newton binomials, with the…

We apply the Desnanot-Jacobi identity to give an alternative proof of the determinants whose entries are rising powers of the Fibonacci numbers given by Prodinger. We then generalize the determinants to include entries that are rising…

We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…

We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions.…