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On a class of Differential Equations whose solutions satisfy Integral Equations

Published online by Cambridge University Press:  20 January 2009

E. T. Whittaker
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The science of the solution of Differential Equations has been in great measure systematized by the aid of ideas borrowed from the Theory of Functions, the equations being classified according to the singularities possessed by their solutions. In the case of linear Differential Equations of the second order

the solutions can have no singularities except at the singularities of the functions q(x) and r(x) (and possibly also at x = ∞ ): these equations may therefore be classified simply according to the number and nature of these singularities.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , February 1914 , pp. 14 - 23
Copyright
Copyright © Edinburgh Mathematical Society 1914

References

* Cf. Proceedings of the International Congress of Mathematicians, Cambridge, 1912.

† Proceedings of the Royal Society of Edinburgh, 1914.

* Two regular singularities now become confluent, and produce an irregular singularity.