Titlebook: Ramanujan’s Notebooks; Part II Bruce C. Berndt Book 1989 Springer-Verlag New York Inc. 1989 Finite.Mathematica.Modular form.integral.proof

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o prove it. Not only are the results fascinating, but, for the most part, Ramanujan‘s methods remaina mystery. Much work still needs to be done. We hope readers will strive to discover Ramanujan‘s thoughts and further develop his beautiful ideas.978-1-4612-8865-7978-1-4612-4530-8

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Infinite Series,l results in Chapter 14, as well as many others as well, aries from a general transformation formula for a large class of analytic Eisenstein series. It should be emphasized, however, that Chapter 14 also contains many other types of results.

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his results were already in the literature, more were not. Almost a decade after Ramanujan‘s death in 1920, G.N. Watson and B.M. Wilson began to edit his notebooks but never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bomba

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Hypergeometric Series, I,rresponds to Chapter 10 of the second notebook, is connected primarily with hypergeometric series. It should be emphasized that Hardy gave only a brief survey of Chapter 12; this chapter contains many interesting results not mentioned by Hardy, and Chapter 10 of the second notebook possesses materia

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Continued Fractions,ely; I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written down by a mathematician of the highest class. They must be true because, if they were not true, no one would have had the imagination to invent them.” These comments

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Integrals and Asymptotic Expansions,sive.” Later he added that Ramanujan’s definite integral formulae “are still interesting and will repay a careful analysis” [9, p. 186]. Indeed, a dismissal of Ramanujan’s contributions to intergration would have beed decidedly premature. First, we might recall that this first letter contained sever

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Book 1989s were already in the literature, more were not. Almost a decade after Ramanujan‘s death in 1920, G.N. Watson and B.M. Wilson began to edit his notebooks but never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957.