(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 (ï¿½ 45)ï¿½ This conception of a limit enables us to deal with algebraical expressions which assume such forms as -° o for particular values of the variable (ï¿½ 39 (iii.)).
} Nx ..., it is clear that, if x,.
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.
+Nxnzk+.., we see that in the term Nx n z k of the development the coefficient N is equal to the number of partitions of n into k parts, with the parts I, 2, 3, 4,, without repetitions.
We see that in the term Nx z of the development the coefficient Nis equal to the number of partitions of n into k parts, with the parts I, 2, 3, 4, ..., with repetitions.
Let somehow or other retardations be introduced so that the optical length of the successive parts increases by the same quantity nX, n being some number and X the wave-length.