Approximations and Asymptotic Expansions

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

Chapter 38 in Ramanujan’s Notebooks, 1998, pp 503-564 from Springer

Abstract: Abstract One of the primary areas to which Ramanujan made fundamental contributions, but for which he received no recognition until recent times, is asymptotic 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 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.

Date: 1998
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DOI: 10.1007/978-1-4612-1624-7_8

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