Related papers: Integrals Involving Associated Laguerre Polynomial…
An umbral type formalism is used to derive integrals involving products of Laguerre polynomials and other special functions.
We give a closed-form expression for the associated Meixner polynomials from which we derive closed-form expressions for the associated Charlier and Laguerre polynomials by a limit procedure. These formulas are then used to derive…
The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using…
Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a method for evaluating new integrals. The method is illustrated by obtaining a closed-form expression for the value of an…
Expressions for the summation of a new series involving the Laguerre polynomials are obtained in terms of generalized hypergeometric functions. These results provide alternative, and in some cases simpler, expressions to those recently…
In a previous paper we deformed Hermite polynomials to three associated polynomials .Here we apply the same deformation to Laguerre polynomials .
In this paper, we study the formulae for a product of two product Euler polynomials. From this study, we derive some formulae for the integral of the product of two or more Ruler polynomials.
We introduce new families of q-deformed 2D Laguerre-Gould-Hopper polynomials. For these polynomials we establish connection formulae which extend some known ones.
We present a number of identities involving standard and associated Laguerre polynomials. They include double-, and triple-lacunary, ordinary and exponential generating functions of certain classes of Laguerre polynomials.
We give integral representations for multiple Hermite and multiple Hermite polynomials of both type I and II. We also show how these are connected with double integral representations of certain kernels from random matrix theory.
Following our earlier work, where doubly indexed and irreducible over Q two-variable Laguerre polynomials were introduced, we prove for such polynomials some recurrence formulas and obtain a generating function. In addition, we show how…
We present results on co-recursive associated Laguerre and Jacobi polynomials which are of interest for the solution of the Chapman-Kolmogorov equations of some birth and death processes with or without absorption. Explicit forms,…
In our investigations on the effect of strong magnetic fields on the properties of elementary particles we have been faced with a definite integral of the form $$\int_0^{2\pi}d\theta\ L_{n}(s^2+t^2+2st\cos\theta)\ e^{-ik\theta}\,…
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…
This contribution aims to obtain several connection formulae for the polynomial sequence, which is orthogonal with respect to the discrete Sobolev inner product \[ \langle f, g\rangle_n=\langle {\bf u}, fg\rangle+ \sum_{j=1}^M \mu_{j}…
In this paper, the conformable Laguerre and associated Laguerre differential equations are solved using the Laplace transform. The solution is found to be in exact agreement with that obtained using the power series. In addition some of…
Expressions for the summation of the series involving the Laguerre polynomials \[S_m(\pm\nu, \pm p)\equiv e^{-x}\sum_{n=0}^\infty \frac{x^n\,L_n^{(\nu)}(x)}{(1\pm \nu\pm p)_n}\frac{(f+m)_n}{(f)_n}\] for any non-negative integers $m$ and $p$…
In this paper, we derive a formula on the integral of products of the higher-order Euler polynomials. By the same way, similar relations are obtained for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler polynomials.…
We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent only for a limited range of parameters. However, when one…
We calculate a double integral over a product of Legendre polynomials multiplied by a binomial raised to a power.