Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the $q$-partial differential equations and $q$-series   Using the theory of functions of several complex variables, we prove that if
an analytic function in several variables satisfies a system of $q$-partial
differential equations, then, it can be expanded in terms of the product of the
Rogers-Szeg\H{o} polynomials. This expansion theorem allows us to develop a
general method for proving $q$-identities. A general $q$-transformation formula
is derived, which implies Watson's $q$-analog of Whipple's theorem as a special
case. A multilinear generating function for the Rogers-Szeg\H{o} polynomials is
given. The theory of $q$-exponential operator is revisited.

22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph