T +ve') TI01 4 0] =eeee TI01 4 0, by replacing each s by
st 4t 4 eeee s and for [ TG +v¢) ¥ by replacing each s

by us .
1+ w')
II[1 + ")

log @ = log IM[1+v/] - log II{1 + "] so that log Q has s' - s

where each s occurs in (7).

For the quotient Q = we know that

TegorBM IX, For an expression of the form
II[1 4 v4') TI[1 4 vg"] ==veee TI[1 4 vyM)
[ + ,,sl“‘)) sesnesenns T[] 4 p, V)

each s in the formulas is replaced by (s' 4 °*** 4 s‘“’).- (s(u“)-f “+s“‘“5.
For [II(1 +v;)I¥ each s is replaced by us, and for

[_II_(-I—:};T)-]v each s is replaced by =-vs. Therefore, for a positive
or negative =, the C's of the expansion of [II(1 +v;)]” are given
by (11) by replacing each s by ns.

For the case of # = -1, dencte the coefficients by C,
(r suggested by "reciprocal”) and the formula is

Z(w +1)my 5 U

n
! 1 ...”q.l 9

=3 ('1) 1

(1700006
T Mt e gl J™ e g1

n n
r‘)‘ sese (g )q’

s,
( JaRgeee JqkgeeeTg

where my =gyt kit >t tri=1, b=+ k4 b, Jgll =g e rel
and where the summation is taken for the indices such that Smghy=r,
Usipg this formula we obtain

3 = 1= +£[(S'+s)~"s ]-xs[("-fs + 3s3)
T + ve0)] = * T oy 1 2 <Sp1 s $152 S3

~ (651501 + 8533) 4 (8S5003)] **eceeeer
Nfben n =<1 and wy(x) = ax, formula (17) reduces to

1 ny Ty

-
(17') Cry 1) Em ij . 'jQ :

]

where ihe summation is taken for the indices such that Smijs=vr,
: ; : Hgei= 1)L L
since mg +1= and j;=h Ang Fople iR il S e
1 Ji Ji i T;fi' Tl 3