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Zbl 0930.65010
Gil, A.; Segura, J.
Evaluation of Legendre functions of argument greater than one. (English)
[J] Comput. Phys. Commun. 105, No.2-3, 273-283 (1997). ISSN 0010-4655

Summary: We present an algorithm to evaluate Legendre functions of the first and second kinds $(P_\nu,Q_\nu)$ for integral and half-integral order and argument greater than one. The code is based on the calculation of the continued fraction for the $Q$'s, the Wronskian relating $P$'s and $Q$'s and the application of forward recurrence relations for the $P$'s and backward recurrence for the $Q$'s. We also show an application of these algorithms to the evaluation of the electrostatic field due to a charged toroidal conductor at potential $V$.

MSC 2000:: *65D20 Computation of special functions
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: toroidal functions; algorithm; Legendre functions; continued fraction; recurrence relations

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