A Mock Theta Function of Second Order

Abstract EN

We consider the second-order mock theta function ?5 (q), which Hikami came across in his work on mathematical physics and quantum invariant of three manifold.

We give their bilateral form, and show that it is the same as bilateral third-order mock theta function of Ramanujan.

We also show that the mock theta function ?5 (q) outside the unit circle is a theta function and also write h1(q) as a coefficient of z0 of a theta series.

First writing h1(q) as a coefficient of a theta function, we prove an identity for h1(q).