On Boole's operational solution of linear finite difference equations with rational coefficients
Published online by Cambridge University Press: 24 October 2008
Extract
The solution of linear differential equations by the method of Frobenius is a straightforward matter consisting merely in the substitution of a power series and obtaining the coefficients from a recurrence relation. The corresponding method when applied to difference equations is laborious and leads in general to divergent series from which convergent solutions can be obtained by a method due to Birkhoff(1). Actually a more appropriate method is to find a factorial series, but even here the direct substitution of such a series requires repeated transformations and throws little light on the structure of the equation. A method of symbolic operators was originated by Boole(2), but owing to the restricted definition of the operators it has a very limited scope. In the present paper a more general interpretation is given to the operators, and their application to a certain class of linear difference equations with rational coefficients is discussed.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 3 , July 1932 , pp. 311 - 318
- Copyright
- Copyright © Cambridge Philosophical Society 1932
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