Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The generalized Abel-Plana formula. Applications to Bessel functions and
  Casimir effect   One of the most efficient methods to obtain the vacuum expectation values for
the physical observables in the Casimir effect is based on the using the
Abel-Plana summation formula. This allows to derive the regularized quantities
by manifestly cutoff independent way and to present them in the form of
strongly converging integrals. However the applications of Abel- Plana formula
in usual form is restricted by simple geometries when the eigenmodes have a
simple dependence on quantum numbers. The author generalized the Abel-Plana
formula which essentially enlarges its application range. Based on this
generalization, formulae have been obtained for various types of series over
the zeros of some combinations of Bessel functions and for integrals involving
these functions. It have been shown that these results generalize the special
cases existing in literature. Further the derived summation formulae have been
used to summarize series arising in the mode summation approach to the Casimir
effect for spherically and cylindrically symmetric boundaries. This allows to
extract the divergent parts from the vacuum expectation values for the local
physical observables in the manifestly cutoff independent way. The present
paper reviews these results. Some new considerations are added as well.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci