Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coupling of the Legendre polynomials with kernels $|x-y|^\alpha$ and
  $\ln|x-y|$   Double integrals that represent matrix elements of the power and logarithmic
potentials in the Legendre polynoiomial basis on [-1,1] are found in a closed
form. Several proofs are given, which involve different special functions and
identities. A connection of the new formulae and Whipple's hypergeometric
summation formula is shown.

20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci