426 
COMPARISON OF THE WEIERSTRASSIAN 
[858 
The form of relation is at once seen to be 
H (u) = Ae Bu *a (Xu), 
and observing that, for u small, we have H (u) = 
2kk'K 
u and <j (Xu) = Xu, we 
have A = 
2kk'K 
; I first write down and afterwards verify the value of B, viz. 
X~7] 
this is =— 4—and the formula thus is 
2 (w 
2kk'K\ 
e 3 " a (Xu). 
In fact, for u writing successively u + 2K, and u 4- 2iK', we obtain 
H (u + 2K) _ K(u+K) or (Xu + 2co) 
H (u) 
a (Xu) ’ 
H(u + 2iK') _-^2)W'(u+iK 1 ) (T (Xu + 2co') 
— c 
H(u) 
which should be satisfied in virtue of 
H(u+2K) 
H(u) 
= -l, 
(Xu) 
a (Xu + 2co) _ {Xu+a) 
a (Xu) 
H(u + 2iK') = CT (Xu 4- 2(o') 2rj'<\W4V) 
H(u) = ’ <7 (Xu) 
viz. we ought to have 
0 = 2K (u + K ) 4- 2r) (Xu + co) 
% (u + iK') = - 2iK' (u + iK') + 2 V ' (Xu + to'). 
JtL CO 
The first of these is 
that is, 
and the second is 
0 = -— (u+K) + U + 0> 
CO \ 
X) ’ 
0 — (— 1 + 1) (u + K) ] 
0 = 
\iK XiK' v 
XK (o 
(u + iK') + 7j' ( U + 
viz. for ire writing 2 (rjco' — rj'co), this is 
0 = 
VC0_-V^_VC0 L + 
CO CO 1 
and the two equations are thus each of them an identity.