Hrycak, Tomasz; Schmutzhard, Sebastian Evaluation of Legendre polynomials by a three-term recurrence in floating-point arithmetic. (English) Zbl 1466.65226 IMA J. Numer. Anal. 40, No. 1, 587-605 (2020). Summary: We prove new error estimates for a three-term recurrence that is used to compute Legendre polynomials. To this end we derive a bilinear representation of the cross-product of Legendre functions and demonstrate estimates of the cross-product that are needed in the error analysis of the recurrence. Cited in 1 Document MSC: 65Q30 Numerical aspects of recurrence relations 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Keywords:Legendre polynomial; Legendre function; three-term recurrence; floating-point arithmetic PDFBibTeX XMLCite \textit{T. Hrycak} and \textit{S. Schmutzhard}, IMA J. Numer. Anal. 40, No. 1, 587--605 (2020; Zbl 1466.65226) Full Text: DOI