Identities involving partial mock theta functions of order five (Q1840492)

The author uses a two parameter generalization of the exponential function defined by \[ E_{q,\beta}^{(\alpha)}(z)=\sum_{n=0}^{\infty} \frac{q^{\alpha n^2/2}z^n}{(q^{\beta};q)_n},\quad\alpha>0 \] to derive some relations between partial sums of the mock theta functions of order five. For the proofs one needs several transformation formulas between these partial sums which are based on the properties of the generalized \(q\)-exponential function \(E_{q,\beta}^{(\alpha)}(z)\) such as \[ E_{q,\beta}^{(\alpha)}(z)-q^{\beta-1}E_{q,\beta}^{(\alpha)}(qz)= q^{\alpha/2}zE_{q,\beta}^{(\alpha)}(q^{\alpha}z). \]