Page:Annales de mathématiques pures et appliquées, 1819-1820, Tome 10.djvu/376

366

INTÉGRATION APPROCHÉE

${\begin{aligned}&-n\left(720+3528n+9744n^{2}+17640n^{3}+21000n^{4}\right.\\&\qquad \left.+15120n^{5}+5040n^{6}\right)\Delta ^{7}q\\&+n\left(5040+26136n+78792n^{2}+162456n^{3}+2325200n^{4}\right.\\&\qquad \left.+231840n^{5}+741120n^{6}+40320n^{7}\right)\Delta ^{8}q\\&-n\left(40320+219168n+708744n^{2}+161481n^{3}\right.\\&\qquad +2693880n^{4}+3265920n^{5}+2731840n^{6}\\&\qquad \left.+1451520n^{7}+362880n^{8}\right)\Delta ^{9}q\\&+n\left(362880+2053152n+7036200n^{2}+17368320n^{3}\right.\\&\qquad +32319000n^{4}+45554560n^{5}+47628000n^{6}\\&\qquad \left.+35078400n^{7}+16329600n^{8}+3628800n^{9}\right)\Delta ^{10}q\\&-n\left(3628800+21257280n+76521456n^{2}+201828000n^{3}\right.\\&\qquad +410031600n^{4}+649479600n^{5}+795175920n^{6}\\&\qquad +731808000n^{7}+479001600n^{8}+199584000n^{9}\\&\qquad \left.+39916800n^{10}\right)\Delta ^{11}q\\&+n\left(39916800+241087680n+905507856n^{2}\right.\\&\qquad +2526193824n^{3}+5519487600n^{4}+9604465200n^{5}\\&\qquad +13293292320n^{6}+14411295360n^{7}+11855289600n^{8}\\&\qquad \left.+6985440000n^{9}+2634508800n^{10}+479001600n^{11}\right)\Delta ^{12}q\\\end{aligned}}$