arXiv subjects

Archna Kumari

Publications and source records attributed to Archna Kumari.

3 recordsLinked to original sources

arXiv2025

Expansion formulas for elliptic hypergeometric series

We provide an alternate approach to obtaining expansion formulas on the lines of the well-poised Bailey lemma. We recover results due to Spiridonov and Warnaar and one new formula of this type. These formulas contain an arbitrary sequence as an argument, and are thus flexible in the number of parameters they contain. As a result, we are able to derive $19$ new transformation formulas for elliptic hypergeometric series. These transformation formulas appear to be new even in the basic hypergeometric case, when $p=0$.

math.NT↗

arXiv2023

An esoteric identity with many parameters and other elliptic extensions of elementary identities

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.

math.NT↗

arXiv2023

A weighted extension of Fibonacci numbers

We extend Fibonacci numbers with arbitrary weights and generalize a dozen Fibonacci identities. As a special case, we propose an elliptic extension which extends the $q$-Fibonacci polynomials appearing in Schur's work. The proofs of most of the identities are combinatorial, extending the proofs given by Benjamin and Quinn, and in the $q$ case, by Garrett. Some identities are proved by telescoping.

math.CO↗