Orthogonal polynomials and continued fractions: from Euler's point of view

2009 ◽  
Vol 46 (09) ◽  
pp. 46-5086-46-5086
Keyword(s):  
Orthogonal Polynomials ◽  
Continued Fractions ◽  
Point Of View

An Application of Separate Convergence for Continued Fractions to Orthogonal Polynomials

1992 ◽  
Vol 35 (3) ◽  
pp. 381-389
Author(s):  
William B. Jones ◽  
W. J. Thron ◽  
Nancy J. Wyshinski
Keyword(s):  
Distribution Function ◽  
Asymptotic Formula ◽  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Continued Fractions ◽  
Polynomial Sequence ◽  
Convergence Results ◽  
Compact Subsets

AbstractIt is known that the n-th denominators Qn (α, β, z) of a real J-fractionwhereform an orthogonal polynomial sequence (OPS) with respect to a distribution function ψ(t) on ℝ. We use separate convergence results for continued fractions to prove the asymptotic formulathe convergence being uniform on compact subsets of

Padé approximants, continued fractions, and orthogonal polynomials

2011 ◽  
Vol 66 (6) ◽  
pp. 1049-1131 ◽  
Author(s):  
Alexander I Aptekarev ◽  
Viktor I Buslaev ◽  
Andrei Martínez-Finkelshtein ◽  
Sergey P Suetin
Keyword(s):  
Orthogonal Polynomials ◽  
Continued Fractions ◽  
Padé Approximants ◽  
Pade Approximants

VI.—On the Graduation of Data by the Orthogonal Polynomials of Least Squares

1934 ◽  
Vol 53 ◽  
pp. 54-78 ◽  
Author(s):  
A. C. Aitken
Keyword(s):  
Orthogonal Polynomials ◽  
Least Squares ◽  
Linear Combination ◽  
Method Of Moments ◽  
Finite Differences ◽  
Continued Fractions ◽  
Selective Bibliography

The problem of fitting a polynomial to data by Least Squares has engaged the attention of many writers. The methods of approach have been many and various. Continued fractions, determinants, the calculus of finite differences and sums, the method of moments, the linear combination of data, the use of the orthogonal polynomials of Legendre and Tchebychef, these and doubtless other instruments of analysis have been pressed into service. At the end of the present paper is given a selective bibliography, which we hope on a future occasion to complete and to supplement by adding brief indications of the standpoint and achievement of each investigator.

scholarly journals The Legacy of Peter Wynn

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1240
Author(s):  
Claude Brezinski ◽  
F. Alexander Norman ◽  
Michela Redivo-Zaglia
Keyword(s):  
Orthogonal Polynomials ◽  
Continued Fractions ◽  
Padé Approximation ◽  
Mathematical Community ◽  
Abstract Algebra ◽  
Moment Problems ◽  
Pade Approximation ◽  
Good Shape ◽  
New Research ◽  
First Time

After the death of Peter Wynn in December 2017, manuscript documents he left came to our knowledge. They concern continued fractions, rational (Padé) approximation, Thiele interpolation, orthogonal polynomials, moment problems, series, and abstract algebra. The purpose of this paper is to analyze them and to make them available to the mathematical community. Some of them are in quite good shape, almost finished, and ready to be published by anyone willing to check and complete them. Others are rough notes, and need to be reworked. Anyway, we think that these works are valuable additions to the literature on these topics and that they cannot be left unknown since they contain ideas that were never exploited. They can lead to new research and results. Two unpublished papers are also mentioned here for the first time.

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