# 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} }

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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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 18 REFERENCES

## and F

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## The orthogonal rational functions of Higgins and Christov and algebraically mapped Chebyshev polynomials

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Ten equivalent definitions of the fractional laplace operator

VIEW 1 EXCERPT

HIGHLY INFLUENTIAL

## Computing Hypergeometric Functions Rigorously

VIEW 1 EXCERPT

## What is the Fractional Laplacian? arXiv:1801.09767v1 [math.NA], 2018

## Multiprecision Computing Toolbox for MATLAB, Version 4.7.0.13560

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL