166 



K. FUJISAWA. 



li=m+\ 



§• 5. 



Let us consider the determinunt 



/.2,»+2^ A--"\ A:2'""^ ... 1, 0, 0, ... 



1, Z, Z\ ... Z"'-^\ S, HZ, ... SZ'"-^ 



1, 2z, ... {:m+\)z"\Ds, Dsz, ... Dsf"-^ 



2 P.iJc' 



2)«+2-2ti 





This determinant is of the sunie form as tlie one in (20.), and we tind 

 likewise 



fi=0 



+ D" 



sz 



^_^^ .A,+ ... +D-,— ^^. A 



sz" 



] 



:(-ir+'y/ii!a-A-2.^y"+2 



D" 



^ J)m-Ti . ^'^ 



^SZ, 



D 



m+l_ 



SZ" 



\-k^z 



Z)"'+-',s, D"'^hz, ... Z)"'+2s^'»-i 



D2'».ç, 



Z)-"'s^, ... D-"\s2'" 



whence 



(•25.) 2 PA'A'2"'+-'-2M = (_iyH+i^2;;i)!!(l-Ä2^')" 



Ln.'^ Lna_l 



Z) 



D 



D" 



2! l-A^^' 8! i-Â;^,^'-U/i+l)! i-Ä;-. 



8! 



B's, 



4! 



DSs, 



■(m + 2) 



:D'«^-,S 



1 



[m+iy ' (m + 2)! 



".s, . . , 



7)2'» s 



