On the connection coefficients and recurrence relations arising from expansions in series of modified generalized Laguerre polynomials: Applications on a semi-infinite domain

Abstract

Herein, three important theorems were stated and proved. The first relates the modified generalized Laguerre expansion coefficients of the derivatives of a function in terms of its original expansion coefficients; and an explicit expression for the derivatives of modified generalized Laguerre polynomials of any degree and for any order as a linear combination of modified generalized Laguerre polynomials themselves is also deduced. The second theorem gives new modified generalized Laguerre coefficients of the moments of one single modified generalized Laguerre polynomials of any degree. Finally, the third theorem expresses explicitly the modified generalized Laguerre coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its modified generalized Laguerre coefficients. Some spectral applications of these theorems for solving ordinary differential equations with varying coefficients and some specific applied differential problems, by reducing them to recurrence relations in their expansion coefficients of the solution are considered.

The Extended Laguerre Polynomials A q , n

“…Dattoli et al [18] applied operational techniques to introduce suitable families of special functions. Andrews et al [19], Trickovic and Stankovic [20], Radulescu [21], and Doha and Youssri [22] have done a lot of work for properties of Laguerre polynomials. Akbary et al [23] can be referred for other applications of Laguerre polynomials.…”

A Class of Laguerre-Based Generalized Humbert Polynomials

“…Classical Laguerre polynomial and its orthogonality [3,4] have been studied extensively. Its generalization is given by the two variable Laguerre polynomial.…”

Compact finite difference method to numerically solving a stochastic fractional advection-diffusion equation

“…Integer order differential equations might not be capable of explaining the experimental and field measurement data, as an alternate approach, the differential fractional-order equation (FDE) is introduced [14][15][16][17][18][19][20][21][22]. Models described by FDEs are now being widely used, and the theory of fractional calculus is a useful mathematical tool for applied science [23][24][25][26].…”