Related papers: Multivariate Bell Polynomials and Derivatives of C…
A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.
In this article, we study the multiple zeta functions (MZF) and some of its variants at identical arguments. Using the harmonic product, these functions can be expressed as polynomials in the Riemann zeta function. Firstly, we note that an…
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…
By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and…
Departing from a class of infinite series with central binomial coefficients in the numerator and depending on a positive integer parameter, we first extend known identities to all complex parameters. Then we use various methods, including…
We use the differential algebra of polytopes to explain the known remarkable relation of the combinatorics of the associahedra and permutohedra with the universal compositional and multiplicative inversion formulas for the formal power…
In this paper, we consider the problem of representing any polynomial in terms of the ordered Bell and degenerate ordered Bell polynomials, and more generally of the higher-order ordered Bell and higher-order degenerate ordered Bell…
A generalized fractional derivative (GFD) definition is proposed in this work. For a differentiable function that can be expanded by Taylor series, we show that D^Elafa*D^Beta f(t)=D^(Elafa+Beta)f(t). GFD is applied for some functions in…
The problem of a differential operator left- and right division is solved in terms of generalized Bell polinomials for nonabelian differential unitary ring. The definition of the polinomials is made by means of recurrent relations. The…
Differential Calculus is a staple of the college mathematics major's diet. Eventually one becomes tired of the same routine, and wishes for a more diverse meal. The college math major may seek to generalize applications of the derivative…
We introduce poly-Bernoulli polynomials in two variables by using a generalization of Stirling numbers of the second kind that we studied in a previous work. We prove the bi-variate poly-Bernoulli polynomial version of some known results on…
In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The…
Graph polynomials are polynomials assigned to graphs. Interestingly, they also arise in many areas outside graph theory as well. Many properties of graph polynomials have been widely studied. In this paper, we survey some results on the…
The multidimensional chain rule formula for analytic functions and its generalisation to higher derivatives perfectly work in the algebraic setting in characteristic zero. In positive characteristic one runs into problems due to…
In this paper, we introduce the degenerate multiple polyexponential functions which are multiple versions of the degenerate modified polyexponential functions. Then we consider the degenerate multi-poly-Genocchi polynomials which are…
In the present paper, by extending some fractional calculus to the framework of Cliffors analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight…
We aim to introduce the generalized multiindex Bessel function $J_{\left( \beta _{j}\right) _{m},\kappa ,b}^{\left( \alpha _{j}\right)_{m},\gamma ,c}\left[ z\right] $ and to present some formulas of the Riemann-Liouville fractional…
In this paper, certain generalized fractional derivative formulae are introduced involving the k-Mittag-Leffler function. Then their image formulae (using Beta transform, Laplace transform and Whittaker transform) are also established. The…
In this paper, we consider the degenerate multi-poly-Bernoulli numbers and polynomials which are defined by means of the multiple polylogarithms and degenerate versions of the multi-poly-Bernoulli numbers and polynomials. We investigate…
Fibonacci polynomials are generalizations of Fibonacci numbers, so it is natural to consider polynomial versions of the various results for Fibonacci numbers. According to Hong, Pongsriiam, Bulawa, and Lee, the generating function of the…