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Evaluation of Legendre polynomials by a three-term recurrence in floating-point arithmetic. (English) Zbl 1466.65226

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.

MSC:

65Q30 Numerical aspects of recurrence relations
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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