In this study, a spectral tau solution to the heat conduction equation is introduced. As basis functions, orthogonal polynomials, namely, shifted fifth-kind Chebyshev polynomials (5CPs), are used. The proposed method’s derivation based on solving integral that corresponds original problem. approach and some theoretical findings serve transform problem with its underlying conditions into suitabl...

1. P. Bateman, J. Kalb, and A. Stenger, A limit involving least common multiples, this MONTHLY 109 (2002) 393–394. doi:10.2307/2695513 2. L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, D. Reidel, DordrechtHolland, 1974. 3. B. Farhi, Nontrivial lower bounds for the least common multiple of some finite sequences of integers, J. Number Theory 125 (2007) 393–411. doi:...

We study generating functions for the number of n-long k-ary words that avoid both 132 and an arbitrary `-ary pattern. In several interesting cases the generating function depends only on ` and is expressed via Chebyshev polynomials of the second kind and continued fractions. 1. Extended abstract 1.1. Permutations. Let Sn denote the set of permutations of [n] = {1, 2, . . . , n}, written in one...

In this paper we describe the use of multivariate Chebyshev polynomials in computing spectral derivations and Clenshaw–Curtis type quadratures. The multivariate Chebyshev polynomials give a spectrally accurate approximation of smooth multivariate functions. In particular we investigate polynomials derived from the A2 root system. We provide analytic formulas for the gradient and integral of A2 ...