Page:Annales de mathématiques pures et appliquées, 1819-1820, Tome 10.djvu/380

 Les corrections sont expliquées en page de discussion

370

INTÉGRATION APPROCHÉE

${\begin{aligned}&+\left(723680+1346625n+1898190n^{2}+1984500n^{3}\right.\\&\qquad \left.+1461600n^{4}+680400n^{5}+151200n^{6}\right)\Delta ^{10}q\\&-\left(8409500+17084650n+27061650n^{2}+33132330n^{3}\right.\\&\qquad +30492000n^{4}+19958400n^{5}+8316000n^{6}\\&\qquad \left.+1663200n^{7}\right)\Delta ^{11}q\\&+\left(105258076+229978650n+400186050n^{2}+553887180n^{3}\right.\\&\qquad +600470640n^{4}+493970400n^{5}+291060000n^{6}\\&\qquad +\left.109771200n^{7}+19958400n^{8}\right)\Delta ^{12}q\\\end{aligned}}$

6.^o Coefficient F.

${\begin{aligned}F&=\Delta ^{5}q-(15+6n)\Delta ^{10}q+\left(175+126n+42n^{2}\right)\Delta ^{7}q\\&-\left(1960+1932n+1176n^{2}+336n^{3}\right)\Delta ^{8}q\\&+\left(22449+27216n+22932n^{2}+12096n^{3}+3024n^{4}\right)\Delta ^{9}q\\&-\left(269325+379638n+396900n^{2}+292320n^{3}\right.\\&\qquad \left.+136080n^{4}+30240n^{5}\right)\Delta ^{10}q\\&+\left(3416930+5412330n+6626466n^{2}+6098400n^{3}\right.\\&\qquad \left.+3991680n^{4}+1663200n^{5}+332640n^{6}\right)\Delta ^{11}q\\&-\left(45995730+80037210n+110777436n^{2}+120094128n^{3}\right.\\&\qquad +98794080n^{4}+58212000n^{5}+21954240n^{6}\\&\qquad \left.+3991680n^{7}\right)\Delta ^{12}q\\\end{aligned}}$