2019/12/23 by Chalifour, Vincent, Grundland, Alfred Michel
#02.40.-k #02.40.Hw #02.40.Ma #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1912.10899
This paper is devoted to a study of the connection between the immersion functions of two-dimensional surfaces in Euclidean or hyperbolic spaces and classical orthogonal polynomials. After a brief description of the soliton surfaces approach defined by the Enneper-Weierstrass formula for immersion and the solutions of the Gauss-Weingarten equations for moving frames, we derive the three-dimensional numerical representation for these polynomials. We illustrate the theoretical results for several examples, including the Bessel, Legendre, Laguerre, Chebyshev and Jacobi functions. In each case, we generate a numerical representation of the surface using the Mathematica symbolic software.