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Recurrence Formulae for the Functions which represent Solutions of the Differential Equation:

Published online by Cambridge University Press:  20 January 2009

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The contents of this paper were suggested by a discussion of the equation:

in a paper by Glaisher which appears in the Philosophical Transactions, 1881, Part III.

The solutions in series of (1) are:

and in the paper referred to it is shewn that the coefficients of hp+1 in the expansions of and of satisfy equation (1) when p is a positive integer.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1914