32 -'^rt. 7. — K. Terazawa : 



„ N 1 \ '2io, 



Making use of the expansion formula ()f the right member, we get 

 vr.-conv) = --""^ jcot-''-^ +4V ?"''"- - . sin "^^ \ . (76) 



The quantity v may l)e calculated by utilizing the Weiersteass' 

 formula to any degree of accuracy,^-* and therefore the value of the 

 function v/^i—w^^(v). The approximate value of this function can, 

 however, be found in tlie following wa}^: 



Put 



and 



1 (ei-ev)H S'(i O-e,)--(gi-e3)'(^(^)-g-)- = ^ 



1 (gj — e.y a.(v) — ( e^ — e^)^ (7;(v) 



2 (e, - ej' (Tjv) + (e, - e.,)* a^v) 



g COS h (/COS + 



l + 2(7^cos "^+2g^«cos ^^" + 



then, since e^ < lf'(tO < «: . we shall liave 



As ç-^ is usually a very small quantity, we may take 



COS — ^ ^ = = s say 



lo, q 



with a close approximation. Since v—co, = dco, purel}' imaginary, 

 Ave ma}^ put 



—^ ^— = IX, 



1) This method has been adopted hy Prof. Xagaoka. I.e. 



2) Halphen, Traité des Fonctions Elliptiques, I. p. 274. 



