Abstract
In the present paper, we consider some variations and generalizations of the multi-sum to single-sum transformation recently used by Rosengren in his proof of the Kanade–Russell identities. These general transformations are then used to prove a number of identities equating multi-sums and infinite products or multi-sums and infinite product \(\times \) a false theta series. Examples include the following:
Let
Then
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Mc Laughlin, J. Some More Identities of Kanade–Russell Type Derived Using Rosengren’s Method. Ann. Comb. 27, 329–352 (2023). https://doi.org/10.1007/s00026-022-00586-3
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DOI: https://doi.org/10.1007/s00026-022-00586-3
Keywords
- Basic hypergeometric series
- Q-series
- Partitions
- q-Products
- Multi-sum identities
- Kanade–Russell identities
- Rogers–Ramanujan identities
- Identities of Rogers–Ramanujan–Slater type
- Capparelli identities