Evaluation of toroidal harmonics (Q1971558)

The authors present three algorithms to evaluate Legendre functions of integral order and half-odd degree of the first and second kind for real arguments larger than one. The first algorithm evaluates the set \(\left\{P^m_{n-{1\over 2}}(x), Q^m_{n-{1\over 2}}(x)\right\}\) for fixed values of \(m\), while the other two algorithms allow obtaining of the set \(\left\{P^m_{n-{1\over 2}}(x), Q^m_{n-{1\over 2}}(x)\right\}\).