160 



R. FUJISAWA. 



th;it is, 



Mm-l) (On A 



(16.) A=(-l) '^ ^■'"'' 



m !! 



'2!^^' 3!^^' {m+l)r ' 



B^o T)i<i D"+-<; 



The expression 



(/;i+l)p'«— .Ai + £)"'6'.A2+ .. + Z)'"s^"'-lA^j 



which occurs on the righthand side of (12.), admits of being simplified 

 in a simiJar manner ; namely denoting, for a moment, this expression 

 by a', we liave 



A'=(m+1) 



D'"^-, D"'.s, D™s.s"'-' 





W !! 



z 



3! ' 



'2 ! ,î- ' 

 1 



4! 



D's,. 



^ -.D"^-^h, ,_ ^.,. Z)"'ns, 



(m + 1)! '(m + 2)! 



1 ^ ,s 



y;t ! /: 



(/yi + '2)! 

 1 



Z)"'+-.s 



(2;;i)! 



D-"''.ç 



Leaving the factor ( — 1)"'+! V^ . ( — 1) ^ .. oat of consideration, 



tlie numerator of the righthand side of e(|ualion (S.) becomes 



