208 ^- FUJISAWA. 



(131) iî,-3= 2''-VH-3)('i'-3'i-6)e^"(''-«'-* 



+ 2^«».0i + 3)(n2 + 3« - 6)c*"<"-=''+'' 



_ 2P-103-' ;i(?i + 1 )(»- + »' - 8)(;r + ^/ - 1 0)e^"*"+i^ 



- 2''-^'n(,n + 3)(?i*- 2;i^ + 2l;r + 42;/ + G0)çirt(n+i)-2 



- 2^-i";i(« - 3)(n*+ 2>i^- 21»-- 42;/. + GO)^'"^""^^^^ 



_ 2^-103 -l;,(;i _ l)(;/2_ Vi _ 8)(;t2- »t - 1 0)ç ^"<"+l^+8 



and thence, by virtue of (111), 



(132) ^,_3=-r3^*''^'-^'>-^ 



+ 2P-^^n{)i - 3)(u* + 2;/^ - 21;r - 42;i + 60)e^"<"-i'-» 

 + 2^^%{n + 3)(«* - 'M + 21 ;r + 42;* + 60)ç^"<"-^'+i 

 + 2^-i''3-ifi(« + 1 )(«- + ;i - 8)(;i2 + n - lO)|^^^"("-i^+5 

 -2^^;<?i + 3)(;r+ 3//-6)e^""'+=""' 

 -2^'-8^;i*-l9;iH 98)ç*"("+="-^ 

 - 2^-^;K;i - 3){)i^ - 3;i - 6)ç^"<'^+=*>+^ 



n'— 9 



Equating the coefficients of a ^ on the two sides of (11<*^), we 

 obtain 



n+2 n— 2 n+2 n— 2 » + 2 «—2 ?i+2 »i— 2 



^Vi+2^'7n-2 - 3 + -^^„+2 - l^'/«-2 - :i + ^q„+2-2^<ln-2 - 1 + ^'/m+2 - 3^'y«-2 



/ >i »I n H \ 



-4(l + fo(2HÄ-2 + Ä,,,_.H,,._,) + Hf'H,,,,H,,.-i- 



When —-y- is even, the lowest power of ^ in the above ecjuation is 

 ^,i>-3rt-2^ Equating the coefficients of this power of ? on the two sides, 

 we get"r3 2''"-2= 2^(^'"-^>, whence 



