An operational approach introduced by Gould and Hopper to the construction of generalized Hermite polynomials is followed in the hypercomplex context to build multidimensional generalized Hermite polynomials by the consideration of an appropriate basic set of monogenic polynomials. Directly related functions, like Chebyshev polynomials of first and second kind are constructed.

We get the computable error bounds for generalized Cornish-Fisher expansions for quantiles of statistics provided that the computable error bounds for Edgeworth-Chebyshev type expansions for distributions of these statistics are known. The results are illustrated by examples.

In this research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main probl...

In this paper, we introduce the class of $(\beta,\gamma)$-Chebyshev functions and corresponding points, which can be seen as a family {\it generalized} Chebyshev polynomials points. For functions, prove that they are orthogonal in certain subintervals $[-1,1]$ with respect to weighted arc-cosine measure. particular investigate cases where become polynomials, deriving new results concerning clas...

The paper extends the applicability of our Matlab package Chebpack to find (generalized) Chebyshev polynomial approximations of the solutions of some Abel integral equations with algebraic singularities. Numerical examples confirm the efficiency of this approach.