We discuss efficient conversion algorithms for orthogonal polynomials. We describe a known conversion algorithm from an arbitrary orthogonal basis to the monomial basis, and deduce a new algorithm of the same complexity for the converse operation.

This paper is concerned with the numerical solution of Volterra integral equations third kind non-smooth solutions based on recursive approach spectral Tau method. To this end, a new set fractional version canonical basis polynomials (called FC-polynomials) introduced. The approximate polynomial Tau-solution) expressed in terms FC-polynomials. structure Tau-solution allows recovering standard d...

The aim of this paper is to construct generating functions for q-beta polynomials. By using these generating functions, we define the q -beta polynomials and also derive some fundamental properties of these polynomials. We give some functional equations and partial differential equations (PDEs) related to these generating functions. By using these equations, we find some identities related to t...

formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...

A full-wave spectral-domain method with an asymptotic extraction technique is formulated for multilayer microstrip lines. This formulation provides a simple closed-form representation of the asymptotic part of the impedance matrix by using Chebyshev polynomial basis functions with the square-root edge condition and the asymptotic behavior of the Green’s function. The formulation is applied to o...