Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Some Integrals Over the Product of Three Legendre Functions   The definite integrals $ \int_{-1}^1(1-x^2)^{(\nu-1)/2}[P_\nu(x)]^3\D x$, $
\int_{-1}^1(1-x^2)^{(\nu-1)/2}[P_\nu(x)]^2P_{\nu}(-x)\D x$,
$\int_{-1}^1x(1-x^2)^{(\nu-1)/2}[P_{\nu+1}(x)]^3\D x $ and
$\int_{-1}^1x(1-x^2)^{(\nu-1)/2}[P_{\nu+1}(x)]^2P_{\nu+1}(-x)\D x $ are
evaluated in closed form, where $P_\nu$ is the Legendre function of degree
$\nu$, and $ \R\nu>-1$. Special cases of these formulae are related to certain
integrals over elliptic integrals that have arithmetic interest.

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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci