Introductio in analysin infinitorum

58 DE EXPLICATIONE FUNCTIONUM LIB. I. Scribatur pro hac Serie ista forma generalis : $1+Az+Bz^2+Cz^3+...+Lz^{n-2}+Mz^{n-1}+Nz^n + \&c.$ atque quilibet coëfficiens ex duobus antecedentibus ita definie- tur ut fit $N = \frac{m-n}{n} \alpha M + \frac{2m-n}{n} \mathfrak{C} L$, unde omnes termini ex primo, qui est 1, definiri poterunt. Erit nempe $A = \frac{m}{1} \alpha;$ $B = \frac{(m-2)}{2} \alpha A + \frac{(2m-2)}{2} \mathfrak{C}$ $C = \frac{(m-3)}{3} \alpha B + \frac{(2m-3)}{3} \mathfrak{C} A$ $D = \frac{(m-4)}{4} \alpha C + \frac{(2m-4)}{4} \mathfrak{C} B$ $\&c.$ 75. Si fuerit $Z = az + \beta z^2 + \gamma z^3$, erit $(1 + az + \beta z^2 + \gamma z^3)^{m-1} = 1 + \frac{(m-1)}{1} (az+\beta z^2+\ [TRUNCATED]