4^4 Aloysii Casinelli 



A, + 2 Ajx-f- 3 A3 jc2 4- 4 A4 x3+ 5 AjX* +6 Aj x* 4, etc. 



■+.A ,a ,x4-2A2rt ix'+SAja , x34.4A4a , a:<4-5 A 5a , x5-|_ etc. 



= •+• A|a2x2_j_2A2a2x3-<-3A3<j2*^+-lA4a2x5-f-eic. 



-t- Aiajx^+SAjajar'-t-BAsaarS-f- etc. 



4- Aia4x'+2A2a4x^-t- etc. 



•4- Ajflsx^-i- etc. 

 Hinc 



2A2-4-Aia|=2ma2+mA,a| 

 3A3-4-2A2(j|-f-Aia2=:3ma3-l-2mAia24-»»iA2a| 

 4Ai-4-3A3ai4-?A2a2+Airt3=::4ma4+SmA(a3-t-2mA2a24-'"A3«| 

 5A5-}-4Aia,4-3A3a2+2A2a3-+-Aia4=i:5ma5-t-4mA|a44-3mA2a34-2mA3aj 



■-t-mAja, 

 6Ag4- SA^flj^- 4A4a2+ BAjas-i- 2A2a4+A|a5=6ma6'-|-5mAia5-J-4mA2«i 

 4-3wA3a3-)-2mA4a2+mA5ai. 



etc. etc. etc. 



ex quibus deducimus 

 Ajzuaim 



A2=:a2/?j4-.J_J.m(m— 1 ) 

 2 



A3=:a3m4-a,a2m(m — 1)H — L_l_lm(m — 1)(m — 2) 

 A4=a4m4-la,a3-f.^jm(m-1)+^l^^m(m— 1)(m-2) 



' "'"'"'"'mC"— ''X'»-2X'"— 3) 



2.3.4 



A5=a5m+(«,a44-a2a3X'»-1)+(^-i^i^^^~^')'"('"-1)('«-2) 

 + ' ' .' V "'-1)-(^-3)+ ' ' ' ' . ' m....(m-4) 



4-1—2 H»i''^«34— 2-3-IH ('"—2) 



/ai<i,a|a3 a,a,a2a2\ , ,, , «iaiaiai' 



-+-I f- — „ ^ Im (m — 3)-t- — 



V 2. 3 2.2 / ^ ; 2.3.4 



ffi....(m— 4) 



