His major work is Exercices de Calcul Intégral, published in three volumes in 1811, 1817 and 1819. In the first volume he introduced the basic properties of elliptic integrals, beta functions and gamma functions, introducing the symbol Γ and normalizing it to Γ(n+1) = n!. Further results on the beta and gamma functions along with their applications to mechanics – such as the rotation of the earth, and the attraction of ellipsoids – appeared in the second volume. In 1830, he gave a proof of Fermat's Last Theorem for exponent n = 5, which was also proven by Lejeune Dirichlet in 1828.
hiS mAjor work IS exERCicEs DE CaLcul intégrAl, PuBliShed in thREE vOluMeS in 1811, 1817 anD 1819. iN the fiRst VoluMe He intRodUceD the basic PropErties oF elLIPtic iNtEGRals, beTA funcTIonS and gamMA fUnCtIons, InTRoducInG thE SYMbol γ and normalIzIng it to Γ(n+1) = N!. fUrthEr ReSuLTs on thE BETa ANd gaMma FunctIoNS AlONG With tHEiR aPPLications to mEChanics – suCh as the RotAtion of THe EarTh, AnD the atTRAction of EllipsOids – APpeared in thE second voLUMe. iN 1830, he gavE a PrOof of fERmat's last theoReM For ExpOneNT n = 5, which Was aLso proVEN By LeJeune Dirichlet in 1828.