In this work, we develop fast algorithms for computations involving finite expansions in Gegenbauer polynomials. We describe a method to convert a linear combination of Gegenbauer polynomials up to degree n into a representation in a different family of Gegenbauer polynomials with generally O(n log(1/ε)) arithmetic operations where ε is a prescribed accuracy. Special cases where source or targe...

It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity Rogers–Ramanujan type, Andrews pointed out classical orthogonal also have surprising applications world q. By introducing Chebyshev third fourth kinds into Bailey pairs, derived a family type identities results related to mock theta function...

In this article, the second kind Chebyshev wavelet method is presented for solving a class of multi-order fractional differential equations (FDEs) with variable coefficients. We first construct the second kind Chebyshev wavelet, prove its convergence and then derive the operational matrix of fractional integration of the second kind Chebyshev wavelet. The operational matrix of fractional integr...

The aim of this paper is to construct non-recursive filters, extensively used type digital filters in signal processing applications, based on Chebyshev orthogonal polynomials. proposes the use fourth-kind polynomials as functions generating new filters. In kind, low-pass with linear phase responses are obtained. Comprenhansive study frequency response characteristics generated filter presented...

The Chebyshev or L∞ estimator minimizes the maximum absolute residual and is useful in situations where the error distribution has bounded support. In this paper, we derive the asymptotic distribution of this estimator in cases where the error distribution has bounded and unbounded support. We also consider the asymptotics of set-membership estimators such as the Chebyshev centre and maximum in...

Ratio asymptotics for matrix orthogonal polynomials with recurrence coefficients An and Bn having limits A and B respectively (the matrix Nevai class) were obtained by Durán. In the present paper we obtain an alternative description of the limiting ratio. We generalize it to recurrence coefficients which are asymptotically periodic with higher periodicity, or which are slowly varying in functio...