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(0, 2) – Interpolation of Entire Functions

Published online by Cambridge University Press:  20 November 2018

R. Gervais ,
Q. I. Rahman  and
G. Schmeisser
R. Gervais
Affiliation:
Université de Montréal, Montréal, Québec
Q. I. Rahman
Affiliation:
Université de Montréal, Montréal, Québec
G. Schmeisser
Affiliation:
Universität Erlangen-Nürnberg, Erlangen, West Germany
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Given a triangular matrix A whose nth row consists of the n points

(1.1)

Turán et al. ([12], [1], [2], [3]) considered the problem of existence, uniqueness, representation, convergence, etc. of polynomials f2n – 1 of degree ≧2n – 1 where the values of f2n – 1 and those of its second derivative are prescribed at the points (1.1), i.e.,

(1.2)

The choice of the points (1.1) is important. They found the zeros

(1.3)

of the polynomial

(1.1)

where Pn – 1 is the (n − 1) Legendre polynomial with the normalization Pn – 1(l) = 1 to be the most convenient.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 5 , 01 October 1986 , pp. 1210 - 1227
Copyright
Copyright © Canadian Mathematical Society 1986

References

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