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  3. Orthogonal Polynomials and Continued Fractions
  • Cited by 36
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2010
      July 2008
      ISBN:
      9780511721403
      9780521854191
      DOI:
      https://doi.org/10.1017/CBO9780511721403
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.86kg, 496 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Number Theory
      Series:
      Encyclopedia of Mathematics and its Applications (122)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Number Theory
    Series:
    Encyclopedia of Mathematics and its Applications (122)
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    Book description

    Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler. This book tells how Euler introduced the idea of orthogonal polynomials and combined the two subjects, and how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polynomials. The most interesting applications of this work are discussed, including the great Markoff's Theorem on the Lagrange spectrum, Abel's Theorem on integration in finite terms, Chebyshev's Theory of Orthogonal Polynomials, and very recent advances in Orthogonal Polynomials on the unit circle. As continued fractions become more important again, in part due to their use in finding algorithms in approximation theory, this timely book revives the approach of Wallis, Brouncker and Euler and illustrates the continuing significance of their influence. A translation of Euler's famous paper 'Continued Fractions, Observation' is included as an Addendum.

    Reviews

    'The range of themes covered is very wide …'

    Source: EMS Newsletter

    'The author has done an admirable job of putting together historical anecdotes and excerpts from original sources with some deep and modern mathematics. The book is a pleasure to read for people interested in either orthogonal polynomials and continued fractions or the history of mathematics, and I imagine that any reader will walk away with a deeper appreciation of both.'

    Source: Mathematical Reviews

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