Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 9.djvu/477

On a ensuite, en portant la précision jusqu’à douze décimales,

${\begin{aligned}\log p=&5{,}400584610947,\\\log q=&5{,}383716651469,\\\log(p+q)=&5{,}693262515480,\end{aligned}}$

d’où l’on tire

${\begin{aligned}\log \left({\frac {p}{p+q}}\right)^{p}=&{\overline {73617}}{,}>6047065,\\\log \left({\frac {q}{p+q}}\right)^{q}=&{\overline {74894}}{,}9259319.\end{aligned}}$

On a pareillement

${\begin{aligned}\log p'=&5{,}867837982735,\\\log q'=&5{,}844451080009,\\\log(p'+q')=&6{,}157331932083,\end{aligned}}$

d’où l’on tire

${\begin{aligned}\log \left({\frac {p'}{p'+q'}}\right)^{p'}=&{\overline {213540}}{,}8676364,\\\log \left({\frac {q'}{p'+q'}}\right)^{q'}=&{\overline {218691}}{,}4253961.\end{aligned}}$

On trouve encore

${\begin{aligned}\log(p+p')=&5{,}995264741371,\\\log(q+q')=&5{,}973544853243,\\\log(p+p'+q+q')=&6{,}285570585161,\end{aligned}}$

d’où l’on tire

${\begin{aligned}\log \left({\frac {p+p'}{p+p'+q+q'}}\right)^{p+p'}=&{\overline {287158}}{,}2327801,\\\log \left({\frac {q+q'}{p+p'+q+q'}}\right)^{q+q'}=&{\overline {293586}}{,}0527612.\end{aligned}}$

On a enfin

${\begin{aligned}\log(1+\mu )=&0{,}2926769,\\\log 2\pi =&0{,}7981799,\end{aligned}}$

partant

${\begin{aligned}\log {\frac {\alpha y'\mathrm {F} {\sqrt {2\pi }}}{\theta }}=&{\overline {580751}}{,}4993272,\\\log k=&{\overline {580745}}{,}0942543,\end{aligned}}$

ce qui donne

${\frac {\alpha y'\mathrm {F} {\sqrt {2\pi }}}{\theta k}}=0{,}0000025414\,;$