Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computation of a numerically satisfactory pair of solutions of the
  differential equation for conical functions of non-negative integer orders   We consider the problem of computing satisfactory pairs of solutions of the
differential equation for Legendre functions of non-negative integer order
$\mu$ and degree $-\frac12+i\tau$, where $\tau$ is a non-negative real
parameter. Solutions of this equation are the conical functions
${\rm{P}}^{\mu}_{-\frac12+i\tau}(x)$ and ${Q}^{\mu}_{-\frac12+i\tau}(x)$,
$x>-1$. An algorithm for computing a numerically satisfactory pair of solutions
is already available when $-1<x<1$ (see \cite{gil:2009:con},
\cite{gil:2012:cpc}).In this paper, we present a stable computational scheme
for a real valued numerically satisfactory companion of the function
${\rm{P}}^{\mu}_{-\frac12+i\tau}(x)$ for $x>1$, the function
$\Re\left\{e^{-i\pi \mu} {{Q}}^{\mu}_{-\frac{1}{2}+i\tau}(x) \right\}$. The
proposed algorithm allows the computation of the function on a large parameter
domain without requiring the use of extended precision arithmetic.

28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con