Numerical Approximation of the Fractional Laplacian on R Using Orthogonal Families

01/23/2020

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by   Jorge Cayama, et al.

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In this paper, using well-known complex variable techniques, we compute explicitly, in terms of the _2F_1 Gaussian hypergeometric function, the one-dimensional fractional Laplacian of the Higgins functions, the Christov functions, and their sine-like and cosine-like versions. After discussing the numerical difficulties in the implementation of the proposed formulas, we develop a method using variable precision arithmetic that gives accurate results.