Description 
1 online resource (xvi, 478 pages) : illustrations 
Series 
Encyclopedia of mathematics and its applications ; 122 

Encyclopedia of mathematics and its applications ; 122.

Contents 
Continued fractions: real numbers  Continued fractions: algebra  Continued fractions: analysis  Continued fractions: Euler  Continued fractions: Euler's influence  Pfractions  Orthogonal polynomials  Orthogonal polynomials on the unit circle  Appendix. Continued fractions, observations L. Euler (1739) 
Summary 
"This new and exciting historical book tells how Euler introduced the idea of orthogonal polynomials and how he combined them with continued fractions, as well as 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."Publisher's description 
Bibliography 
Includes bibliographical references and index 
Notes 
English 

Print version record 
Subject 
Euler, Leonhard, 17071783.


Euler, Leonhard, 17071783 

Orthogonal polynomials.


Continued fractions.


MATHEMATICS  Calculus.


MATHEMATICS  Mathematical Analysis.


Continued fractions


Orthogonal polynomials

Form 
Electronic book

ISBN 
9781107089679 

1107089670 

9780511721403 

0511721404 

1139883267 

9781139883269 

1107101581 

9781107101586 

1107104041 

9781107104044 

1107095980 

9781107095984 

1107092892 

9781107092891 
