-] 8=
where the summation is taken for the values of the exponents such
tbat n+0 + ****+p=0. FEach factor is power of a series of the
form (7). Taking the first,

h =1} @i n
() "h,n - [X i Zi—l%nisdk...r}

nt D)™ wyt 5" Mo )™ my ah n
= Il Tl dakaserrs 1 adE Gy

where the last summation is taken for values of the n's such that

 

Nng+n,+°°"*+ng=n. The other powers of the other u's are similar
to (9). The product uh!" uhf uhq" is formed by taking the sum
cf all the products formed by taking one term from each of the
series like (2) as factors. Bvery term of -;-; is then 2 product of
certain s's with the prcper ccefficient. Let m be any one of the
numbers 0, N, *==, Ny, 8y, Az, -=*, =<2, Py, Pg, **», py . For each
(Sjkeeer)’ in 8 term of the prcduct, there is in its ceefficient
(_1>wm il x"h ; ;
the facter —-—;'——3-.’—"7-'——— The n! in the numerator of (9) is cap=
celled by the denominatcr of (8), and likewise for 6!-<«p! | Inp
each of the expressions like (9) the expenent is separated into
parts such that Ny + Mg + vsov +Ny=n, 6; 4 6, 4 *eee = 8, e,
Py 402+ =p; but in (€) it is required that n+8 + **** 4p =0,
Therefore, in the product it is required that

"!+n2+....+el+62+ oeveld Osl 3 e ik ""+Pk = g

or, in clber terms, My +My+4 ****4+ng = 0. Ncw we obtain
(10)
2Ty Ty Mo nq
"_F s 3 M (-1) Myl T ompl T e gl B )""""(s~ ye
- Al Wel Wl ovy ol QI Leveailne | “daharsory’ - Jehgroery’

where the summaticn is taken for all vslues of the indices which
satisfy the equation nmy +1m, + ****+ng=0, and where by definition
w= 3nghy, and hy = jyx + kB + **°* 4+ r;d . These last operations

i

can be performed to cbtain (1C) because v is a power series (and