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- W2810348009 abstract "In this note, we propose a new class of orthogonal polynomials (named Bachok-Hasham polynomials of the first and second kind for order k, denote it as Z(i,n)k(x), i={ 1,2 }, which is extension of the Chebyshev polynomials of the first and second kind respectively. It is found that Bachok--Hasham polynomials of first and second kind Z(i,n)k(x) are orthogonal with respect to weights w(1,k)(x)=xk−11−x2k, w(2,k)(x)=xk−11−x2k on the interval [-1,1], where k is positive odd integers. Spectral properties Bachok--Hasham polynomials of the first and second kind Z(i,n)k(x),i={ 1,2 } are proved. These properties are used to solve a special class of singular integral equations. Finally, numerical examples and comparison results with other methods are provided to illustrate the effectiveness and accuracy of the proposed method." @default.
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- W2810348009 date "2018-01-01" @default.
- W2810348009 modified "2023-09-23" @default.
- W2810348009 title "Bachok-Hasham polynomials for solving a special class of singular integral equations" @default.
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- W2810348009 doi "https://doi.org/10.1063/1.5041537" @default.
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