01683806

j

01683806 Gil, Amparo Segura, Javier DTORH3 2. 0: A new version of a computer program for the evaluation of toroidal harmonics. Comput. Phys. Commun. 139, No.2, 186-191 (2001). 2001 Elsevier Science B.V. (North-Holland), Amsterdam EN toroidal harmonics Legendre functions Laplace's equation toroidal coordinates program DTORH3 asymptotic expansion

doi:10.1016/S0010-4655(01)00188-6

Summary: An improved version of the program DTORH3 to evaluate toroidal harmonics is presented. The code incorporates a uniform asymptotic expansion for $P^m_\nu(x)$ for large $m$ which extends the range of applicability for large $x$ of the previous version. In addition, the new version of the program takes advantage of the dual behaviour of the function $P$ and $Q$ incorporating a ``dual'' algorithm for $1< x< \sqrt 2$ which improves the accuracy of the code in this range.