  Conical functions appear in a large number of applications in physics and
engineering. In this paper we describe an extension of our module CONICAL for
the computation of conical functions. Specifically, the module includes now a
routine for computing the function ${{\rm R}}^{m}_{-\frac{1}{2}+i\tau}(x)$, a
real-valued numerically satisfactory companion of the function ${\rm
P}^m_{-\tfrac12+i\tau}(x)$ for $x>1$. In this way, a natural basis for solving
Dirichlet problems bounded by conical domains is provided.
