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Expansions in series of Gontcharoff polynomials

Published online by Cambridge University Press:  24 October 2008

G. A. Read
Affiliation:
The Woolwich Polytechnic, London

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)n), 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
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Abel, N. H.Oeuvres d'Abel (1881), t. 2, 6781.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), 473484.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), 222231.Google Scholar