Download e-book for iPad: Orthogonal Polynomials and Continued Fractions: From Euler's by Sergey Khrushchev

By Sergey Khrushchev

persevered fractions, studied because historic Greece, purely turned a robust software within the eighteenth century, within the arms of the good mathematician Euler. This publication tells how Euler brought the assumption of orthogonal polynomials and mixed the 2 matters, and the way Brouncker's formulation of 1655 should be derived from Euler's efforts in distinct capabilities and Orthogonal Polynomials. the main attention-grabbing functions of this paintings are mentioned, together with the good Markoff's Theorem at the Lagrange spectrum, Abel's Theorem on integration in finite phrases, Chebyshev's thought of Orthogonal Polynomials, and intensely contemporary advances in Orthogonal Polynomials at the unit circle. As persevered fractions develop into extra very important back, partially because of their use to find algorithms in approximation thought, this well timed booklet revives the process of Wallis, Brouncker and Euler and illustrates the ongoing value in their impact. A translation of Euler's recognized paper 'Continued Fractions, statement' is integrated as an Addendum.

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Orthogonal Polynomials and Continued Fractions: From Euler's Point of View (Encyclopedia of Mathematics and its Applications) by Sergey Khrushchev

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