and the set called the k's.®® The h's are defined by the equation

1
111 = agx] TI[1 = b4%] TI(1 - Ct_z] exp st ST 7 EY

(L4 hax + hax® 4 200) (L4 hoay+ hogy™ + ***) **vee (1 4 houoi sl 4 housu o 4 *o%)
=14 hax 4 hoay + hocaz + **** + heouoal 4 hox® 4 hyyxy + hygqxe + hoaayz + **oe

+ hooy” + hgeeegz® + *70* 4 hgx® 4 haax®y + hagxy® 4 0+ 4 hyyixys 4 ceere

From the expansion of the second wember and by comparison with the

third, it follows that

hys = hahey, hay = hohoy, **°* hyo = hphgg, *tce h5eeeq = hihos *** hocesq o

Considering that the letters x, y, 2, **** ip the forrula fer the
reciprocal are changed to ~+x, -y, - 2, **** in the definition of
the h's, the expressions (17') for C,, can be changed to correspond

by wultiplying by (~1)", making the signs always positive, Then

1
T g (U hax 4 box® + 2020 ) = 1 = Cyyx 4 Cyga® vvee g (~1)'cr,x' 4 o,
where the C's are given ip terms of the s's by formula (17'). By
making simjlar changes, we find similar expressions for hoy, hoops **%
By multiplying these expressions together we obtain

Tl SR By cesee g LS o Wq
14 to 071 0‘;-", c...'-q

(18) hygeser = 3 vyt ey tr 1 “oe glr 8
where the summation is taken for the indices which satisfy the
equations, Myfy+ Tpia+ ***'= i, T,y 4 Toja 4 *tr= J teeer,
Wyry + Ugry + 0=y ,

Using this formula we obtain
hy= sy, hy= é(saa + 82), hg= gx,‘(safi + 33255 + 354), hgy = é(s,zso, + SgS03)e
By comparison with formula (13), we find that Mijeoer is a sum
which can be selected frow # ...r by making the signs all positive,
It is tc be notices first that each s Has only cne subscript not

*® Maomahon, Vol. II, p, 288, 284,