Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ince's limits for confluent and double-confluent Heun equations   We find pairs of solutions to a differential equation which is obtained as a
special limit of a generalized spheroidal wave equation (this is also known as
confluent Heun equation). One solution in each pair is given by a series of
hypergeometric functions and converges for any finite value of the independent
variable $z$, while the other is given by a series of modified Bessel functions
and converges for $|z|>|z_{0}|$, where $z_{0}$ denotes a regular singularity.
For short, the preceding limit is called Ince's limit after Ince who have used
the same procedure to get the Mathieu equations from the Whittaker-Hill ones.
We find as well that, when $z_{0}$ tends to zero, the Ince limit of the
generalized spheroidal wave equation turns out to be the Ince limit of a
double-confluent Heun equation, for which solutions are provided. Finally, we
show that the Schr\"odinger equation for inverse fourth and sixth-power
potentials reduces to peculiar cases of the double-confluent Heun equation and
its Ince's limit, respectively.

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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int