The Collected Mathematical Papers of Arthur Cayley volume 2
The Collected Mathematical Papers of Arthur Cayley volume 2
Arthur Cayley
The book The Collected Mathematical Papers of Arthur Cayley volume 2 was written by author Arthur Cayley Here you can read free online of The Collected Mathematical Papers of Arthur Cayley volume 2 book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is The Collected Mathematical Papers of Arthur Cayley volume 2 a good or bad book?
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The factor which, equated to zero, gives the prime roots of the equation l-a? = 0. We have i - x m = n [i - x m ], 302 236 RESEARCHES ON THE PARTITION OF NUMBERS. [140 where m denotes any divisor whatever of m (unity and the number m itself not excluded). Hence, if a represent a divisor of one or more of the indices m, and k be the number of the indices of which a is a divisor, we have Now considering apart from the others one of the multiple factors [1 - x a ] k, we may write fx = \\ a?~\ k f .../ x. Suppose that the fraction *j* is decomposed into simpler fractions, in the form fx =I(x} , ^ \ T. . Uw / *"\ S, I* II 1 t "* 1 + &C. , where /(a?) denotes the integral part, and the &c. Refers to the fractional terms depending upon the other multiple factors such as [!-]* The functions 6x are to be considered as functions with indeterminate coefficients, the degree of each such function being inferior by unity to that of the corresponding denominator; and it is proper to remark that the number of the indeterminate coefficients in all the functions 6x together is equal to the degree of the denominator fx.
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