~25-
referring to (7) we see that on one side of the identity each tern

has the form

GLETREE GURE S S e 3

g B
Gt RL eeee g1 o yfl 5\’ Siheseg »
where ja+ M+ ****+d=h, In the definition on page 10 of the
symbol péf ""%fi], it is required that ry/a = J3 e AR X iy

where j,, *°°, 93, wust be integers such that j,‘ is the number of

a's, etc. Then for the array (1'), {p[; “'-txi]}"1 has with it
Tyry Tty
% T~ eeees B x and the product of p's expressed in (15) has
with it a J with the exponent 2 4Taléy eee 4 MG, pulgipjeq
by the other I's with their correspending exponents. In otber words

the terms on the second side of the equation have the form

ceee x % 2 T
n Whahesarqyl  35es U050l o) )

A raz"xfx YBZ"KkK
where the sums are taken for x =1 to « = i, where A depends on
the indices, and where ol¥ngji + B3mek + **°* 4+ ASmac=h, Since
we must use all the values of the indices which satisfy this con~
dition, there is at least one set of numbers such that ZIryejx = j,
Sngkye= k, *t0tt, Imegy . 9, where j, k, ****, g are those given op
the first side of the equation with a certain syi.e.q . Therefore
in the second side of the identity there is a term in %’ b x0
whose coefficient is expressed in p's, for each s YB' Rt I
existing on the first side, Since it is 8n identity in the I's, the
coefficients of the same ficwer on the two sides_are identically
equal.

TaworEw VIII. The fumction s;5,..q can be expressed in
terss of the p's by a formula derived from (7) awd (15), vie.
(16)

A o N gy
Siheeq = (.1) +R¥vee (j+k+ "’éq-l).' m (,11-001) (’j¢"‘n) J

where the summation is taken for values of the indices which