Resonance of Ramanujan's mathematics, Volume 2
This Volume Is In Continuation Of Vol. I And Contains A Critical And Detailed Appraisal Of Ramanujans Work On Theta Functions And Partial Theta Functions, Mock Theta Functions Of Orders Three, Five, Seven And Six (Formally, Designated As Such By Andrews And Hickerson), Lambert Series And Their Relationship With Elliptic Functions, Mock Theta Functions And Allied Functions.A Characteristic Feature Of The Book Is A Detailed Discussion Of The Still Unsettled Problem Of Defining The Order Of A Mock Theta Function And A Discussion Of The Recently Defined Partial Mock Theta Functions And Their Import On Giving New Information On The Structure And Interrelationships Between Mock Theta Functions Of Certain Classes.
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Theta Functions Partial Theta Functions and Ramanujan 1 Introduction
Ramanujans work on theta functions a brief description
Three families of generalised functions associated with mock
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alternative forms Andrews and Hickerson aq/c aq/d associated with mock basic hypergeometric functions basic hypergeometric series bilateral Chapter coefficients convergence deduced definitions denote the number due to Andrews ef/bc fifth order mock functions associated functions of order Garvan generalised functions generalised mock theta given by Ramanujan gives Gupta Hecke type hypergeometric identities integer Lambert series Lemma London Math mock theta conjectures mock theta functions Notebook RLN number of partitions obtain order five order mock theta order three parameters partial fraction partial mock theta partial sums partial theta functions polynomial positive integer power of q Proc proof proved quadratic transformation R.P. Agarwal Ramanujan's Lost remarked replace q result right hand side Rogers-Ramanujan identities root of unity Sears seven mock theta seventh order mock simplification Srivastava summand summation formulae Theorem theta function expansions theta function identities third order mock transformation theory Watson