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An algebraic system of equations with element (n − m)−1, m and n positive unequal integers

Published online by Cambridge University Press:  24 October 2008

A. E. Billington
A. E. Billington
Affiliation:
3 Park Crescent, Fairfield 3078, Victoria, Australia
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Extract

The system of equations here to be analysed is

The method of solution is by way of appeal to the theory of singular integral equations of Cauchy type. Apart from the self-reciprocal series of Titchmarsh(l) no comparable systems appear to have been discussed in the literature, the order of the matrix element falling foul of the restrictions otherwise there imposed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 2 , September 1970 , pp. 415 - 425
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Titchmarsh, E. C.Reciprocal formulae involving series and integrals. Math. Z. 25 (1926), 321–327.CrossRefGoogle Scholar
(2)Muskhelishvili, N. I.Singular integral equations (Groningen, N.V.: P. Woordhoff, 1963).Google Scholar
(3)Whittaker, E. T. and Watson, G. N.Modern analysis (Cambridge University Press, 1946).Google Scholar