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The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks
G. E. Andrews, B. C. Berndt, L. Jacobsen, and R. L. Lamphere
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Memoirs of the American Mathematical Society
1992; 71 pp; softcover
Volume: 99
ISBN-10: 0-8218-2538-0
ISBN-13: 978-0-8218-2538-9
List Price: US$26
Individual Members: US$15.60
Institutional Members: US$20.80
Order Code: MEMO/99/477
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Among his thirty-three published papers, Ramanujan had only one continued fraction, the Rogers-Ramanujan continued fraction. However, his notebooks contain over 100 results on continued fractions. At the end of his second notebook are 100 pages of unorganized material, and the third notebook comprises thirty-three pages of disorganized results. In these 133 pages of material are approximately sixty theorems on continued fractions, most of them new results. In this monograph, the authors discuss and prove each of these theorems. Aimed at those interested in Ramanujan and his work, this monograph will be of special interest to those who work in continued fractions, \(q\)-series, special functions, theta-functions, and combinatorics. The work is likely to be of interest to those in number theory as well. The only required background is some knowledge of continued fractions and a course in complex analysis.

Readership

Researchers in continued fractions, \(q\)-series, special functions, theta-functions, combinatorics, and those interested in number theory as well.

Reviews

"Both the expert and non-expert will profit from studying [the books] contents and will be sure to become Ramanujan fans. It is recommended reading for anyone interested in special functions or approximations and expansions."

-- Journal of Approximation Theory

Table of Contents

  • Abstract
  • Proofs of Entries 1-60
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