Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sturm-Liouville Theory and Orthogonal Functions   We revisit basics of classical Sturm-Liouville theory and, as an application,
recover Bochner's classification of second order ODEs with polynomial
coefficients and polynomial solutions by a new argument. We also outline how a
wider class of equations with polynomial solutions can be obtained by allowing
the weight to become infinite at isolated points:the Jacobi equation, in
general, is of this type. For higher order equations, we also give the basic
analysis required for determining the weight functions and constraints on the
coefficients which make the differential operator defined by the equation self
adjoint for even orders and anti self adjoint in odd orders. We also give
explicit examples of such equations.

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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex