相关论文: $\psi$-Poisson, $q$-Cigler, $\psi$-Dobinski, $\psi…
The normal ordering of an integral power of the number operator in terms of boson operators is expressed with the help of the Stirling numbers of the second kind. As a `degenerate version' of this, we consider the normal ordering of a…
Let $\{X_{n}, n\ge 1\}$ be a sequence of independent random variables with common general error distribution $GED(v)$ with shape parameter $v>0$, and let $M_{n,r}$ denote the $r$th largest order statistics of $X_{1}, X_{2}, \cdots, X_{n}$.…
We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…
We formulate Yang-Mills theory in terms of the large-N limit, viewed as a classical limit, of gauge-invariant dynamical variables, which are closely related to Wilson loops, via deformation quantization. We obtain a Poisson algebra of these…
We derive special forms of the Poisson summation formula for even and odd functions, which are applied to obtain representations for Euler-type numbers and to sum various series related to elliptic functions.
The powers of matrices with Stirling number-coefficients are investigated. It is revealed that the elements of these matrices have a number of properties of the ordinary Stirling numbers. Moreover, "higher order" Bell, Fubini and Eulerian…
We gave a simple derivation of density operator with the quantum analysis. We dealt with the functional of a density operator, and applied maximum entropy principle. We obtained easily the density operators for the Tsallis entropy and…
In this paper, we define and discuss $\mathcal{R}(p,q)$- deformations of basic univariate discrete distributions of the probability theory. We mainly focus on binomial, Euler, P\'olya and inverse P\'olya distributions. We discuss relevant…
Asymptotic behavior (with respect to the number of trials) of symmetric generalizations of binomial distributions and their related entropies are studied through three examples. The first one derives from the q-exponential as a generating…
In this paper, we give some recurrence formula and new and interesting identities for the poly-Bernoulli numbers and polynomials which are derived from umbral calculus.
The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \cite{DPR}. One of the elegant results corresponding with that…
We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…
The distribution of higher order level spacings, i.e. the distribution of $\{s_{i}^{(n)}=E_{i+n}-E_{i}\}$ with $n\geq 1$ is derived analytically using a Wigner-like surmise for Gaussian ensembles of random matrix as well as Poisson…
In this article we generalize the $q$-difference operator due to Carlitz in order to derive explicit sum formulae for several extensions of Stirling numbers of the second kind, including complete homogeneous symmetric functions,…
For basic discrete probability distributions, $-$ Bernoulli, Pascal, Poisson, hypergeometric, contagious, and uniform, $-$ $q$-analogs are proposed.
We present and study a new class of Fock states underlying to discrete electromagnetic Schr\"odinger operators from a multivector calculus perspective. This naturally lead to hypercomplex versions of Poisson-Charlier polynomials, Meixner…
The asymptotic expansion of digamma function is a starting point for the derivation of approximants for harmonic sums or Euler-Mascheroni constant. It is usual to derive such approximations as values of logarithmic function, which leads to…
Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via…
We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function and concepts of the Umbral Calculus associated with it. Also, we present…
This paper introduce a fractional-fractal $\psi$-Fueter operator in the quaternionic context inspired in the concepts of proportional fractional derivative and Hausdorff derivative of a function with respect to a fractal measure. Moreover,…