IV. A certain class of generating functions in the theory of numbers
Open Access
- 31 December 1894
- journal article
- Published by The Royal Society in Philosophical Transactions of the Royal Society of London. (A.)
- Vol. 185, 111-160
- https://doi.org/10.1098/rsta.1894.0004
Abstract
The present investigation arose from my “Memoir on the Compositions of Numbers,” recently read before the Royal Society and now in course of publication in the ‘Philosophical Transactions.' The main theorem may be stated as follows:— If X 1 , X 2 , . . . , X n be linear functions of quantities x 1 , x 2 , . . . . , x n given by the matricular relation (X 1 , X 2 , . . . . . X n ) = ( a 11 a 12 . . a 1 n ) ( x 1 , x 2 , . . . . . , x n ), an a 22 . . a 2 n . . . . . . . . . . a n 1 a n 2 n 3 a nn that portion of the algebraic fraction 1/(1 - s 1 X 1 ) (1 - s 2 X 2 ) . . . . (1 - s n X n )Keywords
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