Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some basic bilateral sums and integrals   By splitting the real line into intervals of unit length a doubly infinite
integral of the form $\Int F(q^x)\,dx,\; 0<q<1$, can clearly be expressed as
$\Integ \Sum F(q^{x+n})\,dx$, provided $F$ satisfies the appropriate
conditions. This simple idea is used to prove Ramanujan's integral analogues of
his \ph{1}{1} sum and give a new proof of Askey and Roy's extention of it.
Integral analogues of the well-poised \ph{2}{2} sum as well as the
very-well-poised \ph{6}{6} sum are also found in a straightforward manner. An
extension to a very-well-poised and balanced \ph{8}{8} series is also given. A
direct proof of a recent q-beta integral of Ismail and Masson is given.

19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph