Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Special functions and spectrum of Jacobi matrices   Several examples of Jacobi matrices with an explicitly solvable spectral
problem are worked out in detail. In all discussed cases the spectrum is
discrete and coincides with the set of zeros of a special function. Moreover,
the components of corresponding eigenvectors are expressible in terms of
special functions as well. Our approach is based on a recently developed
formalism providing us with explicit expressions for the characteristic
function and eigenvectors of Jacobi matrices. This is done under an assumption
of a simple convergence condition on matrix entries. Among the treated special
functions there are regular Coulomb wave functions, confluent hypergeometric
functions, q-Bessel functions and q-confluent hypergeometric functions. In
addition, in the case of q-Bessel functions, we derive several useful
identities.

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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
19
The categories of this paper are: eess