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The Continued Fractions Found in the Unorganized Portions of Ramanujan’s Notebooks
 
The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks
eBook ISBN:  978-1-4704-0903-6
Product Code:  MEMO/99/477.E
List Price: $28.00
MAA Member Price: $25.20
AMS Member Price: $16.80
The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks
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The Continued Fractions Found in the Unorganized Portions of Ramanujan’s Notebooks
eBook ISBN:  978-1-4704-0903-6
Product Code:  MEMO/99/477.E
List Price: $28.00
MAA Member Price: $25.20
AMS Member Price: $16.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 991992; 71 pp
    MSC: Primary 30; 40

    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.

  • Table of Contents
     
     
    • Chapters
    • Proofs of entries 1–60
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 991992; 71 pp
MSC: Primary 30; 40

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.

  • Chapters
  • Proofs of entries 1–60
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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