Description
New Age International (P) Ltd Resonance Of Ramanujan'S Mathematics, Vol. I by Dr. R.P. Agarwal
The present volume contains five chapters on Ramanujan`s work on Generalised Hypergeometric Series-both ordinary and basic, Rogers-Ramanujan type of identities, Definite Integrals-Fourier transform and Self-reciprocal functions, The Master theorem, Beta and Gamma function Integrals and Mordell type of Integrals. Except the four remarkable volumes on Ramanujan`s Notebooks Vol. I-IV by Bruce C. Berndt, there are no other books which give a complete picture of Ramanujan`s work. However, the main thrust of Berndt`s volumes is to give proofs, with adequate references of Ramanujan`s results-entry-wise, as and where they occur in the two Notebooks published by the T.I.F.R. in 1957 and the `Lost` Notebook published in 1988. Since it is well known that the entries in Ramanujan`s Notebooks and the `Lost` Notebook do not necessarily occur topic-wise or in a chronological order, it becomes very difficult to connect the scattered entries and present an elegant, up-to-date version of the development of any particular topic related to Ramanujan and subsequent research workers.
The present work attempts to present an up-to-date, chronological appraisal nd development of certain selected topics in which Ramanujan had made significant contributions. This volume also includes the works of subsequent researchers who were inspired by Ramanujan`s researches. To make the book useful for research workers in these areas, details of methods and proofs of Ramanujan`s results and their generalisations have also been given, wherever considered necessary.