Combinatorial Analysis and Series Inversions

Bruce C. Berndt
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Bruce C. Berndt: University of Illinois, Department of Mathematics

Chapter Chapter 3 in Ramanujan’s Notebooks, 1985, pp 44-84 from Springer

Abstract: Abstract Although no combinatorial problems are mentioned in Chapter 3, much of the content of this chapter belongs under the umbrella of combinatorial analysis. Another primary theme in Chapter 3 revolves around series expansions of various types. However, the deepest and most interesting result in Chapter 3 is Entry 10, which separates the two main themes but which has some connections with the former. Entry 10 offers a highly general and potentially very useful asymptotic expansion for a large class of power series. As with Chapter 2, Ramanujan very briefly sketches the proofs of some of his findings, including Entry 10.

Keywords: Asymptotic Expansion; Nonnegative Integer; Recursion Formula; Polynomial Growth; Bernoulli Number (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-1-4612-1088-7_4

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