Ramanujan-type partial theta identities and conjugate Bailey pairs, II. Multisums

Ramanujan-type partial theta identities and conjugate Bailey pairs, II. Multisums

In the first paper of this series, we described how to find conjugate Bailey pairs from residual identities of Ramanujan-type partial theta identities. Here we carry this out for four multisum residual identities of Warnaar and two more due to the authors. Applying known Bailey pairs gives expressio...

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Veröffentlicht in:The Ramanujan journal 2018-08, Vol.46 (3), p.743-764
Hauptverfasser: Kim, Byungchan, Lovejoy, Jeremy
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
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Zusammenfassung:In the first paper of this series, we described how to find conjugate Bailey pairs from residual identities of Ramanujan-type partial theta identities. Here we carry this out for four multisum residual identities of Warnaar and two more due to the authors. Applying known Bailey pairs gives expressions in the algebra of modular forms and indefinite theta functions.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-017-9919-0