Abstract
We derive a new general transformation for WP-Bailey pairs by considering 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.
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Mc Laughlin, J., Zimmer, P. A reciprocity relation for WP-Bailey pairs. Ramanujan J 28, 155–173 (2012). https://doi.org/10.1007/s11139-011-9349-3
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DOI: https://doi.org/10.1007/s11139-011-9349-3
Keywords
- Bailey pairs
- WP-Bailey chains
- WP-Bailey pairs
- Lambert series
- Basic hypergeometric series
- q-series
- Theta series
- q-products