Open AccessIV. A certain class of generating functions in the theory of numbers
Publication year - 1894
Publication title -
philosophical transactions of the royal society of london. a
Language(s) - English
Resource type - Journals
eISSN - 2053-9231
pISSN - 0264-3820
DOI - 10.1098/rsta.1894.0004
Subject(s) - class (philosophy) , mathematics , combinatorics , algebraic number , memoir , relation (database) , fraction (chemistry) , generating function , discrete mathematics , algebra over a field , pure mathematics , mathematical analysis , philosophy , computer science , chemistry , art , literature , epistemology , organic chemistry , database
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 X1 , X2 , . . . , Xn be linear functions of quantitiesx 1 ,x 2 , . . . . ,xn given by the matricular relation (X1 , X2 , . . . . . Xn ) = (a 11 a 12 . .a 1n ) (x 1 ,x 2 , . . . . . ,xn ),an a 22 . .a 2n . . . . . . . . . .a n 1a n 2n 3 ann that portion of the algebraic fraction 1/(1 -s 1 X1 ) (1 -s 2 X2 ) . . . . (1 -sn Xn )