Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-15T01:32:33.628Z Has data issue: false hasContentIssue false
  • English
  • Français

Expansions in series of Gontcharoff polynomials

Published online by Cambridge University Press:  24 October 2008

G. A. Read
G. A. Read
Affiliation:
The Woolwich Polytechnic, London
Get access Rights & Permissions [Opens in a new window]

Extract

The Gontcharoff polynomials Gn(z; α0, α1,…, αn − 1); n = 0, 1, 2,… are defined to be the polynomials orthogonal to the linear functionals Ln(f) = f(n)(αn), for a specified sequence of complex numbers {αn}. We will abbreviate Gn(z; α0, α1,…, αn−1) to Gn(z) when the sequence {αn} is not in doubt, so that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 699 - 703
Copyright
Copyright © Cambridge Philosophical Society 1968

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Abel, N. H.Oeuvres d'Abel (1881), t. 2, 67–81.Google Scholar
(2)Davis, P. J.Interpolation and approximation (New York, 1965).Google Scholar
(3)Gontcharoff, W.Sur la convergence de la série d'Abel. Mat. Sb. 42 (1935), 473–484.Google Scholar
(4)Macintyre, A. J. and , S. S.Theorems on the convergence and asymptotic validity of Abel's series. Proc. Roy. Soc. Edinburgh Sect. A 63 (1952), 222–231.Google Scholar