Titlebook: Ramanujan’s Notebooks; Part V Bruce C. Berndt Book 1998 Springer Science+Business Media, LLC, part of Springer Nature 1998 Finite.Identity.

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Approximations and Asymptotic Expansions, analysis. Asymptotic formulas, both general and specific, can be found in several places in his second notebook, but perhaps the largest concentration lies in Chapter 13. Several contributions pertain to hypergeometric functions, and an excellent survey of several of these results has been made by

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Infinite Series,elementary and miscellaneous analysis from the material on infinite series, and devoted individual chapters to these three topics. Although those three chapters contain a couple of gems, Chapters 37 and 38 have many more jewels.

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Approximations and Asymptotic Expansions,R. J. Evans [1]. The unorganized pages in the second and third notebooks also contain many beautiful theorems in asymptotic analysis. This chapter is devoted to proving these theorems and a few approximations as well.

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lts had already been published by others, most had not. Almost a decade after Ramanujan‘s death in 1920, G. N. Watson and B. M. Wilson began to edit Ramanujan‘s notebooks, but, despite devoting over ten years to this project, they never completed their task. An unedited photostat edition of the note

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https://doi.org/10.1007/978-1-4612-1624-7Finite; Identity; Invariant; Ramanujan; average; continued fraction; equation; function; theorem

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,Ramanujan’s Theories of Elliptic Functions to Alternative Bases,In his famous paper [3], [10, pp. 23–39], Ramanujan offers several beautiful series representations for 1/pi. He first states three formulas, one of which is.where (a)o = 1 and, for each positive integer ...

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