ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS

doi:10.1016/S0252-9602(15)60004-2

摘要/Abstract

摘要：

Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.

关键词: Chebyshev polynomials of the third and fourth kinds, expansion coefficients, generalized hypergeometric functions, boundary value problems

Abstract:

Key words: Chebyshev polynomials of the third and fourth kinds, expansion coefficients, generalized hypergeometric functions, boundary value problems

中图分类号:

42C10

Eid H. DOHA, Waleed M. ABD-ELHAMEED, Mahmoud A. BASSUONY. ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS[J]. 数学物理学报(英文版), 2015, 35(2): 326-338.

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