Pagina:Werkecarlf03gausrich.djvu/208

V. Termini quinque, ${\textstyle n=4.}$

${\textstyle {\begin{array}{rlrl}&U^{\phantom {\prime }}=u^{5}-{\frac {10}{9}}u^{3}+{\frac {5}{21}}u\\&U^{\prime }=u^{4}-{\frac {7}{9}}uu+{\frac {64}{945}}\\&T^{\phantom {\prime }}=t^{5}-{\frac {5}{2}}t^{4}+{\frac {20}{9}}t^{3}-{\frac {5}{6}}tt+{\frac {5}{42}}t-{\frac {1}{252}}&&\\&T^{\prime }=t^{4}-2t^{3}+{\frac {47}{36}}tt-{\frac {11}{36}}t+{\frac {137}{75600}}&&\\&\;\;\quad a^{\phantom {\prime \prime \prime \prime }}=0{,}0469100770\;\;306680&&\\&\;\;\quad a^{\prime {\phantom {\prime \prime \prime }}}=0{,}2307653449\;\;471585&&\\&\;\;\quad a^{\prime \prime {\phantom {\prime \prime }}}=0{,}5&&\\&\;\;\quad a^{\prime \prime \prime {\phantom {\prime }}}=0{,}7692346550\;\;528415&&\\&\;\;\quad a^{\prime \prime \prime \prime }=0{,}9530899229\;\;693320&&\\&R^{\phantom {\prime \prime }}={R}^{\prime \prime \prime \prime }=0{,}1184634425\;\;280945&\log .=&9{,}0735843490\\&{R}^{\prime {\phantom {\prime }}}={R}^{\prime \prime \prime {\phantom {\prime }}}=0{,}2393143352\;\;496832&=&9{,}3789687142\\&R^{\prime \prime }={\frac {64}{225}}^{\phantom {\prime }}=0{,}2844444444\;\;444444&=&9{,}4539974559\end{array}}}$

Expressio generalis horum coëfficientium, excluso ${\textstyle {R}^{\prime \prime },}$

${\textstyle -{\frac {91}{400}}uu+{\frac {1099}{3600}}}$

Correctio proxime ${\textstyle ={\frac {1}{698544}}L^{\scriptscriptstyle X}}$

VI. Termini sex, ${\textstyle n=5.}$

${\textstyle {\begin{array}{rlrl}U^{\phantom {\prime }}=&u^{6}-{\frac {15}{11}}u^{4}+{\frac {5}{11}}uu-{\frac {5}{231}}\\U^{\prime }=&u^{5}-{\frac {34}{33}}u^{3}+{\frac {1}{5}}u\\T^{\phantom {\prime }}=&t^{6}-3t^{5}+{\frac {75}{22}}t^{4}-{\frac {20}{11}}t^{3}+{\frac {5}{11}}tt-{\frac {1}{22}}t+{\frac {1}{924}}\\T^{\prime }=&t^{5}-{\frac {5}{2}}t^{4}+{\frac {74}{33}}t^{3}-{\frac {19}{22}}tt+{\frac {29}{220}}t-{\frac {7}{1320}}\\&a^{\phantom {\prime \prime \prime \prime \prime }}=0{,}0337652428\;\;984240\\&a^{\prime {\phantom {\prime \prime \prime \prime }}}=0{,}1693953067\;\;668678\\&a^{\prime \prime {\phantom {\prime \prime \prime }}}=0{,}3806904069\;\;584015\\&a^{\prime \prime \prime {\phantom {\prime \prime }}}=0{,}6193095930\;\;415985\\&a^{\prime \prime \prime \prime {\phantom {\prime }}}=0{,}8306046932\;\;331322\\&a^{\prime \prime \prime \prime \prime }=0{,}9662347571\;\;015760\\R^{\phantom {\prime \prime }}=&R^{\prime \prime \prime \prime \prime }=0{,}0856622461\;\;895852\quad \log .=8{,}9327894580\\R^{\prime {\phantom {\prime }}}=&R^{\prime \prime \prime \prime {\phantom {\prime }}}=0{,}1803807865\;\;240693\quad {\phantom {\log \;\,=.}}9{,}2561902763\\R^{\prime \prime }=&R^{\prime \prime \prime {\phantom {\prime \prime }}}=0{,}2339569672\;\;863455\quad {\phantom {\log \;\,=.}}9{,}3691359831\end{array}}}$

Coëfficientium expressio generalis

${\textstyle -{\frac {77}{800}}u^{4}-{\frac {7}{75}}uu+{\frac {23}{96}}}$

Correctio proxime ${\textstyle ={\frac {1}{11099088}}L^{\scriptscriptstyle XII}}$