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Published online by Cambridge University Press: 20 January 2009
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.
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