The Final Problem : An Account of the Mock Theta Functions

Ramanujan’s Lost Notebook

“…In 1934, Hardy passed on to Watson a considerable amount of his material on Ramanujan. However, it appears that either Watson did not possess the "lost" notebook in 1936 and 1937 when he published his papers [289], [290] on mock theta functions, or he had not examined it thoroughly. In any event, Watson [289, p. 61], [81, p. 330] writes that he believes that Ramanujan was unaware of certain third order mock theta functions and their transformation formulas.…”

“…The only identities of this nature from the lost notebook that we exclude are most of those examined by Watson in [289]. It should be noted that in [24], several results were proved by a much clumsier technique.…”

Bijective Proofs of a Theorem of Fine and Related Partition Identities

“…which was asserted by Ramanujan [2] and proved by Watson [7]. We denote by DE the set of partitions σ into an even number of distinct parts such that σ 2i−1 = σ 2i + 1 for i = 1, .…”

“…226 A. J. YeeFig. 3. n = 5, ((4, 3, 3, 1),(5,5,4,4,4,1), (5, 4, 3, 2, 1)) ↔ ((9, 9, 7, 4, 3, 3, 1),(7,6)). …”

A Note on Certain Properties of Mock Theta Functions of Order Eight

“…Later on Andrews (1976) rediscovered Ramanujan's lost note book found in the library of Trinity college Cambridge, which contains many further results on Mock theta functions, certain unresolved problems, and their possible future interest and relationship in the general context of the basic hypergeometric theory. In the first phase of development G. N. Watson [22], R. P. Agrawal [3,4,5,6] and G. E. Andrews [1,2] had contributed significantly. The emergence of Ramanujan's Lost Notebook offered a new platform for further devel opment in the literature of Mock theta functions and consequently Choi [7], Gordon and McIntosh [12] provide valuable information regarding the structure and possi ble construction of new Mock theta functions other than ones given by Ramanujan.…”