Q-Series Transformation Formulae And Rogers-Ramanujan Type Identities

In this thesis, by making use of different methods, many new Rogers-Ramanujan type identities and q-series transformation formulae have been established. The main contents of this dissertation are listed as follows:In the first chapter, combining Bailey's transform with several identities in Verma and Jain [87], we obtain some new q-series transformation formulae and generalize one Singh's result [81]. Then, specializing some parameters of the transformation formulae, we derive many new multiple Rogers-Ramanujan type identities.As the special format of Bailey's transform, Bailey's Lemma plays an important role in many fields. In the second chapter, using some q-series transformation formulae obtained before, we construct several new Bailey pairs. Inserting these Bailey pairs in Bailey's Lemma, many new Rogers-Ramanujan type identities are derived. Besides, we also insert some Bailey pairs in interative Bailey's Lemma and obtain a lot of new Rogers-Ramanujan type identities.In the third chapter, by employing generating function technique, we establish several recurrence relations of some summations. Then the results in [91] are generalized by these recurrence relations and some q-series identities. Furthermore, many new Rogers-Ramanujan type identities are obtained.In the last chapter, on the one hand, based on Carlitz inversions, we establish several Carlitz inversion chains, by which we obtain some q-series transformation formulae; on the other hand, by means of Abel's method and an identity of Jackson, we establish several finite bilateral q-series transformation formulae with differrent independent bases. Furthermore, the dual summation formulae are also given.