Gaurav Bhatnagar,
Archna Kumari, and
and Michael J. Schlosser
An esoteric identity with many parameters and
other elliptic extensions of elementary identities
(16 pages)
Abstract.
We provide elliptic extensions of elementary identities such as the sum of
the first n odd or even numbers, the geometric sum and the sum of the
first n cubes. Many such identities, and their q-analogues,
are indefinite sums, and can be obtained from telescoping. So we used
telescoping in our study to find elliptic extensions of these identities.
In the course of our study, we obtained an identity with many parameters,
which appears to be new even in the q-case. In addition, we recover
some q-identities due to Warnaar.
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