An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order

DOI10.1016/j.jcp.2018.01.014zbMath1395.65005arXiv1707.03287OpenAlexW2735804434MaRDI QIDQ1640835

James Bremer

Publication date: 14 June 2018

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.03287

zbMATH Keywords

fast algorithmsasymptotic methodsspecial functionsassociated Legendre functionsbutterfly algorithmsnonoscillatory phase functions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Computation of special functions and constants, construction of tables (65D20)

Related Items (6)

Phase function methods for second order linear ordinary differential equations with turning points ⋮ A unified framework for oscillatory integral transforms: when to use NUFFT or butterfly factorization? ⋮ Rapid Application of the Spherical Harmonic Transform via Interpolative Decomposition Butterfly Factorization ⋮ Multidimensional phase recovery and interpolative decomposition butterfly factorization ⋮ On the efficient evaluation of the azimuthal Fourier components of the Green's function for Helmholtz's equation in cylindrical coordinates ⋮ Sphere and disk partition functions in Liouville and in matrix integrals

Uses Software

• mctoolbox
• DLMF
• libsharp

Cites Work

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• Accuracy and Stability of Numerical Algorithms
• Butterfly Factorization
• On the convergence of multiple Fourier series
• Interpolative Butterfly Factorization
• ON THE CHOICE OF STANDARD SOLUTIONS FOR A HOMOGENEOUS LINEAR DIFFERENTIAL EQUATION OF THE SECOND ORDER

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