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A Determinantal Expansion for a Class of Definite Integral

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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We have shown in [1] that under certain conditions the definite integral may be approximated by a determinantal ratio. It is our object now to develop the theory when C (x) is a polynomial, showing the relation to the continued fraction form for . In particular we shall give various forms for the approximants, and an integral form for the numerator.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 10 , Issue 3 , January 1956 , pp. 134 - 140
Copyright
Copyright © Edinburgh Mathematical Society 1956

References

REFERENCES

1.Shenton, L. R., “A determinantal expansion for a class of definite integral, Part 1,” Proc. Edinburgh Math. Soc. (2), 9 (1953), 44–52.CrossRefGoogle Scholar
2.Stieltjes, Thomas Jan, Recherches sur les fractions continue! Chapter VIII (Oeuvres Complètes, Tome II).Google Scholar
3.J., Geronimus, “On some persymmetric determinants,” Journal London Math. Soc., 6 (1931), 55–59.Google Scholar