Infinite Series

Bruce C. Berndt
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Bruce C. Berndt: University of Illinois at Urbana-Champaign, Department of Mathematics

Chapter 37 in Ramanujan’s Notebooks, 1998, pp 409-502 from Springer

Abstract: Abstract In the last two chapters devoted to the second and third notebooks, we gather together most of Ramanujan’s results on series in the 133 pages of unorganized material found in these two notebooks. In this chapter, we primarily focus on exact formulas, while in Chapter 38 our attention is given to approximations and asymptotic formulas. In Part IV [4], we had disengaged Ramanujan’s results on special functions, partial fraction decompositions, and 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.

Keywords: Positive Integer; Eisenstein Series; Simple Polis; Infinite Series; Summation Formula (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1624-7_7

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DOI: 10.1007/978-1-4612-1624-7_7

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