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About the Cover: The Continued Fraction of Rogers–Ramanujan

About the Cover: The Continued Fraction of Rogers–Ramanujan Computational Methods and Function Theory (2019) 19:1–2 https://doi.org/10.1007/s40315-019-00261-4 About the Cover: The Continued Fraction of Rogers–Ramanujan Elias Wegert © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Keywords Holomorphic function · Continued fraction · Phase plot Mathematics Subject Classification 30B70 · 11Y65 Introduction In his famous paper [3] of 1894, Leonhard Rogers introduced and studied the continued fraction 1/5 R(z) = . (1) 1 + 1 + 1 + 1 + Rogers proved convergence for |z| < 1 and derived the product representation 5n−1 5n−4 (1 − z )(1 − z ) 1/5 R(z) = z . 5n−2 5n−3 (1 − z )(1 − z ) n=0 About 20 years later, in his first two letters to Hardy ([5], pp. xxvii f.), Srinivasa Ramanujan made several claims about R. In his notebooks [4] and his “lost note- book” [6], he recorded an enormous number of evaluations and theorems. Many of these have been established rigorously only much later—and a few turned out to be erroneous (see Berndt and Rankin [2]). B Elias Wegert wegert@math.tu-freiberg.de Institute of Applied Analysis, TU Bergakademie Freiberg, 09596 Freiberg, Germany 123 2 E. Wegert Fig. 1 The continued fraction of Rogers–Ramanujan (middle) and two of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

About the Cover: The Continued Fraction of Rogers–Ramanujan

Computational Methods and Function Theory , Volume 19 (1) – Feb 16, 2019

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Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-019-00261-4
Publisher site
See Article on Publisher Site

Abstract

Computational Methods and Function Theory (2019) 19:1–2 https://doi.org/10.1007/s40315-019-00261-4 About the Cover: The Continued Fraction of Rogers–Ramanujan Elias Wegert © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Keywords Holomorphic function · Continued fraction · Phase plot Mathematics Subject Classification 30B70 · 11Y65 Introduction In his famous paper [3] of 1894, Leonhard Rogers introduced and studied the continued fraction 1/5 R(z) = . (1) 1 + 1 + 1 + 1 + Rogers proved convergence for |z| < 1 and derived the product representation 5n−1 5n−4 (1 − z )(1 − z ) 1/5 R(z) = z . 5n−2 5n−3 (1 − z )(1 − z ) n=0 About 20 years later, in his first two letters to Hardy ([5], pp. xxvii f.), Srinivasa Ramanujan made several claims about R. In his notebooks [4] and his “lost note- book” [6], he recorded an enormous number of evaluations and theorems. Many of these have been established rigorously only much later—and a few turned out to be erroneous (see Berndt and Rankin [2]). B Elias Wegert wegert@math.tu-freiberg.de Institute of Applied Analysis, TU Bergakademie Freiberg, 09596 Freiberg, Germany 123 2 E. Wegert Fig. 1 The continued fraction of Rogers–Ramanujan (middle) and two of

Journal

Computational Methods and Function TheorySpringer Journals

Published: Feb 16, 2019

References