l<;2 ^- FUJISAWA. 



((32) B,, = i-iy.VS, ...C2n-2i-l)C2/yZ,,_,+ ... 



+ (-lr.l.3....(2;i-2r-lX'2/)%,_,+ ... + 1.8. ...(2,i-l)Z„ , 

 where 



fn-2rfr /n-2r-l/r-2/ / /t-2r-2/")-4r2 

 /f'0\ ry _ yi 72 ■ ./l 72 ./s J ./ 1 Ji J-i 1 



\K^ö) z/„_, (,i_2?-)!/-!'^(/i-2r+l)!(r-2)!l!"^(«-2/-+2)!(r-4)!2'. ■" ' 

 the lust term iDeing 



accordinii' as /■ is even or odd. 



Observe that both .S„ and //„ are rational integral functions of z of the 

 degree 2/<. 



§ K'- 



The determinant-expressions of § <S, simple as they niav a])pear, 

 are not convenient for introducing .S„ and Yi',, of the last section. It 

 is desirable to derive the multiplication-formulce in forms slightly 

 different from those given in § 8. 



Consider first the case n odd. Referring to § '1^ we might Iku'c 



p 

 taken yi} instead of /'+''^As' and then we shajl ha\'e in [)lace of (5) 



the following determinant : 



