Related papers: Lah numbers and Laguerre polynomials of order nega…
The aim of this paper is to introduce the degenerate generalized Laguerre polynomials as the degenerate version of the generalized Laguerre polynomials and to derive some properties related to those polynomials and Lah numbers, including an…
In this paper we introduce and study two generalizations of Lah numbers, analogous to the Stirling numbers with higher level - a combinatorial one (Lah numbers with higher level) and an algebraic one (Lah numbers of order $s$). We define…
Expressions for the derivatives of the Legendre polynomials of the first kind with respect to the order of these polynomials are given. An explicit form for the fourth derivative is presented.
In this paper, we study a class of sequences of polynomials linked to the sequence of Bell polynomials. Some sequences of this class have applications on the theory of hyperbolic differential equations and other sequences generalize…
We introduce a 'grading switching' for arbitrary nonassociative algebras of prime characteristic p, aimed at producing a new grading of an algebra from a given one. We take inspiration from a fundamental tool in the classification theory of…
In this paper, we introduce the Lah-Bell numbers and their natural extensions, namely the Lah-Bell polynomials, and derive some basic properties of such numbers and polynomials by using elementary methods. In addition, we consider the…
In this paper, we focus on computing the higher slope Hasse polynomials of L-functions of certain exponential sums associated to the following family of Laurent polynomials $f(x_1,\ldots ,x_{n+1})=\sum_{i=1}^na_i…
In this note we compare two formulas for the higher order derivatives of the function 1/(exp(x) -1). We also provide an integral representation for these derivatives and obtain a classical formula relating zeta values and Bernoulli numbers.
An interesting discovery in the last two years in the field of mathematical physics has been the exceptional $X_\ell$ Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms,…
In a previous paper we deformed Hermite polynomials to three associated polynomials .Here we apply the same deformation to Laguerre polynomials .
In this note, by using the Hasse-Teichm\"uller derivatives, we obtain two explicit expressions for the related numbers of higher order Appell polynomials. One of them presents a determinant expression for the related numbers of higher order…
In this paper, we study the degenerate Eulerian polynomials and numbers and give some new and interesting identities associated with several special numbers and polynomials.
Exceptional orthogonal Laguerre polynomials can be viewed as an extension of the classical Laguerre polynomials per excluding polynomials of certain order(s) from being eigenfunctions for the corresponding exceptional differential operator.…
Laguerre and Laguerre-type polynomials are orthogonal polynomials on the interval $[0,\infty)$ with respect to a weight function of the form $w(x) = x^{\alpha} e^{-Q(x)}, Q(x) = \sum_{k=0}^m q_k x^k, \alpha > -1, q_m > 0$. The classical…
Generic Newton polygons for L-functions of exponential sums associated to Laurent polynomials in one variable are determined. The corresponding Hasse polynomials are also determined.
Recently, Daehee numbers and polynomials are introduced by the authors. In this paper, we consider the Daehee numbers and polynomials of order k and give some relation between Daehee polynomials of order k and special polynomials
We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (X_{\ell}) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly…
We introduce the associated Lah numbers. Some recurrence relations and convolution identities are established. An extension of the associated Stirling and Lah numbers to the r-Stirling and r-Lah numbers are also given. For all these…
The aim of this paper is to present the construction of exceptional Laguerre polynomials in a systematic way, and to provide new asymptotic results on the location of the zeros. To describe the exceptional Laguerre polynomials we associate…
A previous study of exactly solvable rationally-extended radial oscillator potentials and corresponding Laguerre exceptional orthogonal polynomials carried out in second-order supersymmetric quantum mechanics is extended to $k$th-order one.…