On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials

2003 ◽  
Vol 36 (20) ◽  
pp. 5449-5462 ◽  
Author(s):  
E H Doha
Keyword(s):  
Recurrence Relations ◽  
Laguerre Polynomials ◽  
Connection Coefficients ◽  
In Series

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

2019 ◽  
Vol 8 (1) ◽  
pp. 318-327 ◽  
Author(s):  
E.H. Doha ◽  
Y.H. Youssri
Keyword(s):  
Recurrence Relations ◽  
Laguerre Polynomials ◽  
Infinite Domain ◽  
Laguerre Expansion ◽  
Varying Coefficients ◽  
Generalized Laguerre Polynomials ◽  
General Order ◽  
In Series ◽  
Expansion Coefficients ◽  
Derivatives Of

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.

scholarly journals NEW RECURSIVE APPROXIMATIONS FOR VARIABLE-ORDER FRACTIONAL OPERATORS WITH APPLICATIONS

2018 ◽  
Vol 23 (2) ◽  
pp. 227-239 ◽  
Author(s):  
Mahmoud A. Zaky ◽  
Eid H. Doha ◽  
Taha M. Taha ◽  
Dumitru Baleanu
Keyword(s):  
Recurrence Relations ◽  
Laguerre Polynomials ◽  
Collocation Methods ◽  
Fractional Integrals ◽  
Variable Order ◽  
Spectral Collocation ◽  
Fractional Differential ◽  
Derivatives Of ◽  
Spectral Collocation Methods ◽  
Numerical Approaches

To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation.In this paper, we develop Laguerre spectral collocation methods for solving variable-order fractional initial value problems on the half line. Specifically, we derive three-term recurrence relations to efficiently calculate the variable-order fractional integrals and derivatives of the modified generalized Laguerre polynomials, which lead to the corresponding fractional differentiation matrices that will be used to construct the collocation methods. Comparison with other existing methods shows the superior accuracy of the proposed spectral collocation methods.

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