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Evaluation of Legendre functions of argument greater than one. (English) Zbl 0930.65010
Summary: We present an algorithm to evaluate Legendre functions of the first and second kinds (P ν ,Q ν ) 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:
65D20Computation of special functions, construction of tables
33C45Orthogonal polynomials and functions of hypergeometric type