New fifth and seventh order mock theta function identities (Q2299103)

In the paper under review, the author gives simple proofs of Hecke-Rogers indefinite binary theta series identities for the two Ramanujan's fifth order mock theta functions \(\chi_0(q):= \sum_{n=0}^{\infty} \frac{q^n}{(q^{n+1};q)_n} \) and \(\chi_1(q):= \sum_{n=0}^{\infty} \frac{q^n}{(q^{n+1};q)_{n+1}} \) and all three of Ramanujan's seventh order mock theta functions. It is a nice and surprising result that the coefficients of the three mock theta functions of order \(7\) are related. The proof is based on some conjugate Bailey pair and Heine's transformation.