Sentence Examples


  • (b) If nx >o, (1+x).
  • Thus we arrive at the differential coefficient of f(x) as the limit of the ratio of f (x+8) - f (x) to 0 when 0 is made indefinitely small; and this gives an interpretation of nx n-1 as the derived function of xn (� 45)� This conception of a limit enables us to deal with algebraical expressions which assume such forms as -° o for particular values of the variable (� 39 (iii.)).
  • } Nx ..., it is clear that, if x,.
  • =n, then we have in the development of the product a term x n, and hence that in the term Nx of the product the coefficient N is equal to the number of partitions of n with the parts I, 2, 3, ..., without repetitions; or say that the product is the generating function (G.
  • Observing that any factor 1/I-x l is=l+x l +x 2l +..., we see that in the term Nx the coefficient is equal to the number of partitions of n, with the parts I, 2,, ..,withh repetitions.
 

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