Page:Joseph Louis de Lagrange - Œuvres, Tome 5.djvu/443

ensuite

${\begin{alignedat}{2}r''[r',r'']\,\ =&0{,}299570\qquad \qquad &\log .\quad &9{,}4764990,\\r''[r',r'']_{1}=&0{,}088745&&8{,}9481444,\\r''[r',r'']_{2}=&0{,}0195694&&8{,}2915777,\\r''[r',r'']_{3}=&0{,}004778&&7{,}6792282,\\r''[r',r'']_{4}=&0{,}001200&&7{,}0793117,\\r''[r',r'']_{5}=&0{,}000239&&6{,}3776848,\\\ldots \ldots \ldots \ldots &\ldots \ldots \ldots &&\ldots \ldots \ldots \,;\end{alignedat}}$

enfin

${\begin{alignedat}{2}2r''^{2}{\frac {d[r',r'']}{dr''}}\,\ =&0{,}027810\qquad \qquad &\log .\quad &8{,}4442010,\\2r''^{2}{\frac {d[r',r'']_{1}}{dr''}}=&0{,}189855&&9{,}2784220,\\2r''^{2}{\frac {d[r',r'']_{2}}{dr''}}=&0{,}081339&&8{,}9102988,\\2r''^{2}{\frac {d[r',r'']_{3}}{dr''}}=&0{,}029561&&8{,}4707191,\\2r''^{2}{\frac {d[r',r'']_{4}}{dr''}}=&0{,}010255&&8{,}0109357,\\2r''^{2}{\frac {d[r',r'']_{5}}{dr''}}=&0{,}0041349&&7{,}6164650,\\\ldots \ldots \ldots \ldots \ldots &\ldots \ldots \ldots &&\ldots \ldots \ldots .\end{alignedat}}$

7. Or, $n$ étant comme dans le n^o 4 égal à

$1-z^{\frac {3}{2}},$

on aura

$n=0{,}841432\,;$

et, faisant ces substitutions dans la formule du n^o 1 après y avoir changé $r,p,\mathrm {T}$ en $r',p',\mathrm {T} ',$ il viendra

$-\mathrm {T} '\left[0,126279\sin(p''-p')-0{,}070377\sin 2(p''-p')-0{,}006104\sin 3(p''-p')\right.$

$\left.-0{,}000883\sin 4(p''-p')-0{,}000142\sin 5(p''-p')-\ldots \right],$