First, write simply 
-n + l 
Then we get consecutively 
-2p^;_2 
- = (r V _i 
- r\/^n_i = n 
({n + l)x^ 
^ /y>n + 2 y*’* 
i(n-l) f + 1)(^ + 2)^^ g ?^(?^ - l)x'^ 
^ /I + 3 ^71 + 1 
“2 (?^- 2)(n — ^ 
*■ ^n~l 
|_32^p3'y_4^ -(rv^)^w_i 
-T?fa-nfa o'.l' 0 *+l)(» + 2 )(” + 3)x“ An + \)n{n-\)^-‘^ 
' ^m+4 + 2 
_ 2 (?^ - l)(?^ - 2)(?^ - 3)^” -^ - 3)(7i - 4)(7^ - 5)x^-^'i 
91 — 2 ^ 
and similarly for the consecutive coefficients, and, in fact, 
the general form can be established in the usual method. 
From these Vo, U_i, &c., can be found consecutively. 
Thus pV„ = ^„ 
m-2- 
( ^n-2\ 
- |_^2V®V-2 = :^^?^ - 1 . - 2| 
n+lx^ n — K>x^~^\ 
y.n + 2 ■*■' 
m — 2 j 
- |3 2yu. 
?^.?^-l.?^-2.?^-3 
{n + ^.n-\-2x^ ^n.n-lx'^-'^ 
y.w + 3 
+ 1 
+ 3 
7^ - 2 . n- Zx^ n- A: . n - 5x^ ~ 
^n — l 
y>n-Z 
|42^p^V— 4 = n , n - \ . n — 2 . n — Z . n- A + 
o?-t-l . '?^^-2. n + Zx^^ .n+ln. n + lx'^^' 
fpfh -f- 2 
y*Tl + 4 
f,n- \ . n-’i , n - Zx'^ + ^ ,?^,-3.^-4.?^- Zx'^ 
+ 6 ;s ^ ;srr2 
n - 5 . n- Z . n- 7x'^~^' 
M — 4 
and the general term may also be established. 
