Corpus ID: 210911852

Numerical Approximation of the Fractional Laplacian on $\mathbb R$ Using Orthogonal Families

@inproceedings{Cayama2020NumericalAO,
  title={Numerical Approximation of the Fractional Laplacian on \$\mathbb R\$ Using Orthogonal Families},
  author={Jorge Cayama and Carlota M. Cuesta and Francisco de la Hoz},
  year={2020}
}
  • Jorge Cayama, Carlota M. Cuesta, Francisco de la Hoz
  • Published 2020
  • Mathematics, Computer Science
  • In this paper, using well-known complex variable techniques, we compute explicitly, in terms of the 2F1 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. 

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