Page:Annales de mathématiques pures et appliquées, 1820-1821, Tome 11.djvu/304

290

ÉQUATIONS

${\begin{aligned}+{\tfrac {ce^{-\beta x}}{\beta (\beta +\alpha )}}+{\tfrac {2bcx}{\alpha (\beta ^{2}-\alpha ^{2})}}&+\ldots +b^{2m-1}c\left(A_{2m,1,0}+A_{2m,1,1}x\right)e^{2(m-1)\beta x}\\+{\tfrac {c^{2}e^{-2\beta x}}{\beta .2\beta (\beta -\alpha )(2\beta -\alpha )}}&+\ldots \ldots \ldots \ldots \ldots \ldots \ldots \\&+b^{m}c^{m}\left(A_{2m,m,0}+A_{2m,m,1}x+\ldots +A_{2m,m,m}x^{m}\right)\\&+b^{m-1}c^{m+1}\left(A_{2m,m+1,0}+A_{2m,m+1,1}+\ldots +A_{2m,m+1,m-1}\right)e^{-2\beta x}\\&+\ldots \ldots \ldots \ldots \ldots \ldots \ldots \\&+c^{2m}A_{2m,2m,0}e^{-2m\beta x}\\&+b^{2m+1}A_{2m+1,0,0}e^{(2m+1)\beta x}+\ldots \ldots \\&+b^{2m}c\left(A_{2m+1,1,0}+A_{2m+1,1,1}x\right)e^{(2m-1)\beta x}+\ldots \ldots \\&+\ldots \ldots \ldots \ldots \ldots \ldots \ldots \\&+b^{m+1}c^{m}\left(A_{2m+1,m,0}+A_{2m+1,m,1}x+\ldots +A_{2m+1,m,m}x^{m}\right)e^{\beta x}+\ldots \\&+\ldots \ldots \ldots \ldots \ldots \ldots \ldots \\&+bc^{2m}\left(A_{2m+1,2m,0}+A_{2m+1,2m,1}x\right)e^{(1-2m)\beta x}+\ldots \\&+c^{2m+1}A_{2m+1,2m+1,0}e^{-(2m+1)\beta x}+\ldots \\\end{aligned}}$