Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the derivative of the associated Legendre function of the first kind
  of integer degree with respect to its order   The derivative of the associated Legendre function of the first kind of
integer degree with respect to its order, $\partial
P_{n}^{\mu}(z)/\partial\mu$, is studied. After deriving and investigating
general formulas for $\mu$ arbitrary complex, a detailed discussion of
$[\partial P_{n}^{\mu}(z)/\partial\mu]_{\mu=\pm m}$, where $m$ is a
non-negative integer, is carried out. The results are applied to obtain several
explicit expressions for the associated Legendre function of the second kind of
integer degree and order, $Q_{n}^{\pm m}(z)$. In particular, we arrive at
formulas which generalize to the case of $Q_{n}^{\pm m}(z)$ ($0\leqslant
m\leqslant n$) the well-known Christoffel's representation of the Legendre
function of the second kind, $Q_{n}(z)$. The derivatives $[\partial^{2}
P_{n}^{\mu}(z)/\partial\mu^{2}]_{\mu=m}$, $[\partial
Q_{n}^{\mu}(z)/\partial\mu]_{\mu=m}$ and $[\partial
Q_{-n-1}^{\mu}(z)/\partial\mu]_{\mu=m}$, all with $m>n$, are also evaluated.

21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex