T T M P A N O R fM. 457 



meros impares fumere licet , ex qiiorum fingulis infi- 

 niti valores pro a , ideoque infiniti foni, exfurgunt. 



18. Verum haec feries tantum integrale parti- 

 culare noftrae aequationis difFercntio - difFerentialis cxhi- 

 bet , cum vnicam conflantem arbitrariam inuoluat ; fe- 

 ries autem duas conflantes ab arbitrio nof^ro pendentes 

 reperietur , fi ponatur i iz: pfin. ^-t-^cof.7^ , ac tum 

 aequationis refultantis partes tam per fin. 7^ quam cor.^*^ 

 afFedas feorfim nihilo aequentur , mdeque quantitates p 

 et q per feries definiantur. Calculo hoc fubdudlo , fi 

 breuitatis gratia ponamus ^ — &, vt Ci r:^;^ ^, ma- 

 neatque « n: 2 p -+- ^ , erit 



«_--i-rPfin.e(A-|->>i9- TUTZi.T} ,.,(.-t-.)(n-^-.) ■ 



(ii-f-i )( n-t-4)(n-i-6)Afl* ^ 



-~r- ,. ,,.(n_j_,],„_j-,)(n_,_3) -1- etc^ 



V .,0 ,-^r A/^f A /5 ('i-+-5)9l«« , (n-+-2)( B-+ .«)A9» 



^ rP cof. ( ^4 - A ^ - ^i^.r -^ r7(^T)or;r7) 



(" -f-_i_) (n->- «;)(n-f-<;) 5N^ ^ \ 



'>' 2. J.+ (n -f. ,) (^-l-2)(n-+-T) etC.j 



vbi, vt ante, obferuandum efi, loco (3 nonnifi numeros 

 integros accipi poffe \ tum autem crit 2;~«fin.(a/+'y) 

 fin.(p(P-4- (5) at A et 5i ^nnt binae conRantes arbi- 

 trariae per duplicem integrationem introdudae. Qiiodfi 

 ergo breuitatis gratia ponamus : 



^ ":(«-!-')'' 2-3.+(H-^-iXn-t-2)('i-f3)'" 2.3-4.5.6;fi-t->)(r!.+-j)(n-t-i);n-»-4)\n+.i) I ^lC. — r 

 " 2.i{n-^-\){n-i-i) ~i~ 3.3.,.5(n_j-,)(n-+-j)(Ti-f-jX'i-H4) *"" ^^^* — X. 



habebimus : 



i/ — yP(APfin.^-i-5(Q_fin.e-f-S(Pcof.^-Aqcofe). 



Tom.X.Nou.Comm. Kk Si 



