Bailey pairs and indefinite quadratic forms. II: False indefinite theta functions (Q2122584)

We construct families of Bailey pairs \((\alpha_n,\beta_n)\) where the exponent of \(q\) in \(\alpha_n\) is an indefinite quadratic form, but where the usual \((-1)^j\) is replaced by a sign function. This leads to identities involving ``false'' indefinite binary theta series. These closely resemble \(q\)-identities for mock theta functions or Maass waveforms, but the sign function prevents them from having the usual modular properties.