Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously the author proved the first six of Ra-manujan's tenth order mock theta function identities. It is the purpose of this paper to prove the seventh and eighth identities of Ramanujan's tenth order mock theta function identities which are expressed by mock theta functions and a definite integral. L. J. Mordell's transformation formula for the definite integral plays a key role in the proofs of these identities. Also, the properties of modular forms are used for the proofs of theta function identities.

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S. Ramanujan introduced the mock theta functions in his last letter to G.H. Hardy. In his letter and Lost Notebook, he presented mock theta functions and their identities. The expression of each mock theta function relies on the hypergeometric series. G.N. Watson studied the relations between Ramanujan's fifth order mock theta functions and the function introduced by M. Lerch in 1893. In this manuscript, we develop the relations between the basic bilateral hypergeometric series and the functions deduced from all mock theta functions introduced by

Ramanujan's lost notebook contains many results on mock theta functions. In particular, the lost notebook contains eight identities for tenth order mock theta functions. Previously, the author proved six of the eight tenth order mock theta function identities. It is the purpose of this paper to prove the fifth and sixth identities of Ramanujan's tenth order mock theta functions. The properties of modular forms are used for the proofs of theta function identities.