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A Determinantal Expansion for a Glass of Definite Integral1. Part 1

Published online by Cambridge University Press:  20 January 2009

L. R. Shenton
L. R. Shenton
Affiliation:
College of Technology, Manchester, 1.
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1. Let w(x) be a non-negative weight function for the finite interval (a, b) such that exists and is positive, and let Tr(x), r = 0, 1, 2,…be the corresponding orthonormal system of polynomials. Then if F(x) is continuous on (a, b) and has “Fourier” coefficients

Parseval's formula gives

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 1 , October 1953 , pp. 44 - 52
Copyright
Copyright © Edinburgh Mathematical Society 1953

References

2 See for example Jackson, D., Fourier Series and Orthogonal Polynomials (Carus Math. Mon., 1941), Ch. II, and p. 228Google Scholar, or Szegö, G., Orthogonal Polynomials (New York, 1939), Ch. III.CrossRefGoogle Scholar

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