caa a22 4500 463178254 CHVBK 20180406164831.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s11139-006-0241-5 doi (NATIONALLICENCE)springer-10.1007/s11139-006-0241-5 A reciprocity theorem for certain q -series found in Ramanujan's lost notebook [Elektronische Daten] [Bruce Berndt, Song Chan, Boon Yeap, Ae Yee] Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan's lost notebook. The first proof uses Ramanujan's 1ψ1 summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares. Springer Science + Business Media, LLC, 2006 q -series nationallicence Reciprocity theorem nationallicence Ramanujan's 1ψ1 summation theorem nationallicence Quintuple product identity nationallicence Sums of three squares nationallicence Combinatorial bijection nationallicence Berndt Bruce Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, Illinois aut Chan Song Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, Illinois aut Yeap Boon Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, Illinois aut Yee Ae Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, Illinois aut The Ramanujan Journal Kluwer Academic Publishers 13/1-3(2007-06-01), 27-37 1382-4090 13:1-3<27 2007 13 11139 https://doi.org/10.1007/s11139-006-0241-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-006-0241-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Berndt Bruce Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, Illinois aut NATIONALLICENCE 700 1- Chan Song Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, Illinois aut NATIONALLICENCE 700 1- Yeap Boon Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, Illinois aut NATIONALLICENCE 700 1- Yee Ae Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, Illinois aut NATIONALLICENCE 773 0- The Ramanujan Journal Kluwer Academic Publishers 13/1-3(2007-06-01), 27-37 1382-4090 13:1-3<27 2007 13 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer