The search for differential equations for certain sets of orthogonal polynomials

The Search for Differential Equations for Certain Sets of Orthogonal Polynomials

We look for differential equations of the form ∞ ∑ i=0 ci(x)y (x) = 0, where the coefficients {ci(x)} ∞ i=0 are continuous functions on the real line and where {ci(x)} ∞ i=1 are independent of n, for the generalized Jacobi polynomials { P n (x) } ∞ n=0 and for generalized Laguerre polynomials { L n (x) } ∞ n=0 which are orthogonal with respect to an inner product of Sobolev type. We use a metho...

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...

The Search for Differential Equations for Orthogonal Polynomials by Using Computers

We look for differential equations of the form ∞ ∑ i=0 ci(x)y (x) = λny(x), where the coefficients {ci(x)} ∞ i=0 do not depend on n, for the generalized Jacobi polynomials { P n (x) } ∞ n=0 found by T.H. Koornwinder in 1984 and for generalized Laguerre polynomials { L n (x) } ∞ n=0 which are orthogonal with respect to an inner product of Sobolev type. We introduce a method which makes use of co...

A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

Differential and Difference Equations for Products of Classical Orthogonal Polynomials