Related papers: A note on infinite series whose terms involve trun…
Integrals involving derivatives of Legendre polynomials frequently arise in applications ranging from multipole expansions for processes involving electromagnetic probes to spectral methods in numerical physics. Despite their practical…
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 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…
Adaptive dimensionality reduction in high-dimensional problems is a key topic in statistics. The multiplicative gamma process takes a relevant step in this direction, but improved studies on its properties are required to ease…
We present explicit formulae for q-exponentials on quantum spaces which could be of particular importance in physics, i.e. the q-deformed Minkowski-space and the q-deformed Euclidean space with two, three or four dimensions. Furthermore,…
In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.
We consider products of $q$-gamma functions with rational arguments, and prove several $q$-generalizations of recent works concerning products of gamma functions. In particular, we consider products indexed by Dirichlet characters, and…
Our paper is devoted to several problems from the field of modified divisors: namely exponential and infinitary divisors. We study the behaviour of modified divisors, sum-of-divisors and totient functions. Main results concern with the…
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
The aim of this paper is by using generating functions to further study some identities and properties on the degenerate Stirling numbers of the second kind, the degenerate $r$-Stirling numbers of the second kind, the degenerate Stirling…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
The main objective of this article is to study the exponential sums associated to Fourier coefficients of modular forms supported at numbers having a fixed set of prime factors. This is achieved by establishing an improvement on…
A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…
Finite trigonometric sums appear in various branches of Physics, Mathematics and their applications. For p; q to coprime positive integers and r we consider the finite trigonometric sums involving the product of three trigonometric…
The purpose of this article is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
These notes are devoted to the theory of exponential sums over finite fields. The first chapter recalls some of the number-theoretic interest of such sums. The second chapter discusses the $L$-functions attached to such sums, the "Weil…
This article gives a brief introduction to $q$-special functions, i.e., $q$-analogues of the classical special functions. Here $q$ is a deformation parameter, usually $0<q<1$, where $q=1$ is the classical case. The main topics to be treated…
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
Let Y be a random variable whose degenerate moment generating functions exist in some neighborhoods of the origin. The aim of this paper is to study the probabilistic degenerate Stirling numbers of the first kind associated with Y which are…
We study flat deformations of quotients of a polynomial algebra in a class of graded commutative associative algebras. Functional equations and their solutions in terms of theta functions play important role in these studies. An analog of…