A Reciprocity Relation for WP-Bailey Pairs
Number Theory
2019-01-10 v1
Abstract
We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Other consequences include new proofs of some classical identities due to Jacobi, Ramanujan and others, and indeed extend these identities to identities involving particular specializations of arbitrary WP-Bailey pairs.
Cite
@article{arxiv.1901.02872,
title = {A Reciprocity Relation for WP-Bailey Pairs},
author = {James Mc Laughlin and Peter Zimmer},
journal= {arXiv preprint arXiv:1901.02872},
year = {2019}
}
Comments
17 pages