Introductio in analysin infinitorum

RECURRENTIBUS. 185 CAP. XIII. 222. Seriei ergo quae oritur ex hac fractione $\frac{A+Bpz}{(1 - 2pz \cos \Phi + p^2 z^2)^3}$ terminus generalis erit hic $\frac{A p^n z^n}{16 (\sin \Phi)^5} ( \frac{(n+5)(n+4)}{1 \cdot 2} \sin(n+1)\Phi - \frac{2(n+1)(n+5)}{1 \cdot 2} \times$ $\sin(n+3)\Phi + \frac{(n+1)(n+2)}{1 \cdot 2} \sin(n+5)\Phi )$ $+ \frac{B p^n z^n}{16 (\sin \Phi)^5} ( \frac{(n+4)(n+3)}{1 \cdot 2} \sin n\Phi - \frac{2n(n+4)}{1 \cdot 2} \sin(n+2)\Phi +$ $\frac{n(n+1)}{1 \cdot 2} \sin(n+4)\Phi )$. Atque, ulterius progrediendo, Seriei, quae oritur ex hac fractione $\frac{A+Bpz}{(1 - 2pz \cos \Phi + p^2 z^2)^4}$ terminus generalis erit hic $+ [TRUNCATED]