Related papers: $\kappa$-generalization of Stirling approximation …

We show how the asymptotic expansion for the gamma function $\Gamma(x)$, similar to that obtained by Boyd [Proc. Roy. Soc. London A447 (1994) 609--630], can be obtained by using a form of Lagrange's inversion theorem with a remainder. A…

In this note the Polyakov equation [Phys. Rev. E {\bf 52} (1995) 6183] for the velocity-difference PDF, with the exciting force correlation function $\kappa (y)\sim1-y^{\alpha}$ is analyzed. Several solvable cases are considered, which are…

Here we consider the degenerate Bernstein polynomials as a degenerate version of Bernstein polynomials, which are motivated by Simsek's recent work 'Generating functions for unification of the multidimensional Bernstein polynomials and…

We consider the generators $L_k$ of Heckman-Opdam diffusion processes in the compact and non-compact case in $N$ dimensions for root systems of type $A$ and $B$, with a multiplicity function of the form $k=\kappa k_0$ with some fixed value…

The p-adic Kummer--Leopoldt constant kappa\_K of a number field K is (assuming the Leopoldt conjecture) the least integer c such that for all n \textgreater{}\textgreater{} 0, any global unit of K, which is locally a p^(n+c)th power at the…

The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…

We denote by kappa the implicit signature that contains the multiplication and the (omega-1)-power. It is proved that for any completely kappa-reducible pseudovariety of groups H, the pseudovariety DRH of all finite semigroups whose regular…

In the present effort we show that $S_{\kappa}=-k_B \int d^3p (n^{1+\kappa}-n^{1-\kappa})/(2\kappa)$ is the unique existing entropy obtained by a continuous deformation of the Shannon-Boltzmann entropy $S_0=-k_B \int d^3p n \ln n$ and…

We show that an interesting class of functionals of stochastic differential equations can be approximated by a Chen-Fliess series of iterated stochastic integrals and give a L^{2} error estimate, thus generalizing the standard stochastic…

We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with such numbers. Using various identities for Stirling numbers…

Elliptic functions are largely studied and standardized mathematical objects. The two usual approaches are due to Jacobi and Weierstrass. From a contour integral which allowed us to unify many summation formulae (Euler-MacLaurin, Poisson,…

We describe, in an algebraic way, the $\kappa$-deformed extended Snyder models, that depend on three parameters $\beta, \kappa$ and $\lambda$, which in a suitable algebra basis are described by the de Sitter algebras ${o}(1,N)$. The…

In this article, we study the local behaviour of the multiple zeta functions at integer points and write down a Laurent type expansion of the multiple zeta functions around these points. Such an expansion involves a convergent power series…

Factorial series played a major role in Stirling's classic book "Methodus Differentialis" (1730), but now only a few specialists still use them. This article wants to show that this neglect is unjustified, and that factorial series are…

Given a stochastic matrix $P$ partitioned in four blocks $P_{ij}$, $i,j=1,2$, Kemeny's constant $\kappa(P)$ is expressed in terms of Kemeny's constants of the stochastic complements $P_1=P_{11}+P_{12}(I-P_{22})^{-1}P_{21}$, and…

We provide a model where u(\kappa) < 2^{\kappa} for a supercompact cardinal \kappa. Garti and Shelah have provided a sketch of how to obtain such a model by modifying the construction in a paper of Dzamonja and Shelah; we provide here a…

In [9], the celebrated K{\L}-inequality has been extended from definable functions $f:\mathbb{R}^{n}\rightarrow\mathbb{R} $ to definable multivalued maps $S:\mathbb{R}\rightrightarrows\mathbb{R}^{n}$, by establishing that the co-derivative…

We use the Jacobi-Trudi formula to execute "explicit" evaluation of determinants of Stirling numbers of both kinds. We also offer a Maple package accompanying the paper on the personal websites at the end of the second page.

We present Lie-algebraic deformations of Minkowski space with undeformed Poincar\'{e} algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of noncommutative coordinates in terms of…

In this paper, we consider the normalized Bessel function of index $\alpha > -\frac{1}{2}$, we find an integral representation of the term $x^nj_{\alpha+n}(x)j_\alpha(y)$. This allows us to establish a product formula for the generalized…