TY - JOUR
T1 - PARTIAL INDEFINITE THETA IDENTITIES
AU - Kim, Byungchan
AU - Lovejoy, Jeremy
N1 - Publisher Copyright:
© 2016 Australian Mathematical Publishing Association Inc.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - Using a result of Warnaar, we prove a number of single- and multi-sum identities in the spirit of Ramanujan's partial theta identities, but with partial indefinite binary theta functions in the role of partial theta functions. We also calculate the corresponding residual identities and use a result of Ji and Zhao to recast our identities in terms of indefinite ternary theta functions.
AB - Using a result of Warnaar, we prove a number of single- and multi-sum identities in the spirit of Ramanujan's partial theta identities, but with partial indefinite binary theta functions in the role of partial theta functions. We also calculate the corresponding residual identities and use a result of Ji and Zhao to recast our identities in terms of indefinite ternary theta functions.
KW - Bailey pairs
KW - indefinite theta functions
KW - partial indefinite theta functions
KW - partial theta functions
UR - https://www.scopus.com/pages/publications/84988420031
U2 - 10.1017/S1446788716000318
DO - 10.1017/S1446788716000318
M3 - Article
AN - SCOPUS:84988420031
SN - 1446-7887
VL - 102
SP - 255
EP - 289
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
IS - 2
ER -