Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T14:27:43.956Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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