  Ramanujan's lost notebook contains many mock theta functions and mock theta
function identities not mentioned in his last letter to Hardy. For example, we
find the four tenth-order mock theta functions and their six identities. The
six identities themselves are of a spectacular nature and were first proved by
Choi. We also find eight sixth-order mock theta functions in the lost notebook,
but among their many identities there is only a single relationship like those
of the tenth-orders. Using Appell function properties of Hickerson and
Mortenson, we discover and prove three new identities for the sixth-order mock
theta functions that are in the spirit of the six tenth-order identities. We
also include an additional nineteen tenth-order like identities for various
combinations of second-, sixth-, and eighth-order mock theta functions.
