Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/103

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}386343,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}942413,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}527589,\\b_{\frac {1}{2}}^{(3)}&=0{,}323359,&b_{\frac {1}{2}}^{(4)}&=0{,}206811,&b_{\frac {1}{2}}^{(5)}&=0{,}135616,\\b_{\frac {1}{2}}^{(6)}&=0{,}090412,&b_{\frac {1}{2}}^{(7)}&=0{,}061101,&b_{\frac {1}{2}}^{(8)}&=0{,}041731\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=1{,}643709,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=2{,}272414,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=2{,}069770,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=1{,}738781,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=1{,}407491,&{\frac {db_{\frac {1}{2}}^{(5)}}{d\alpha }}&=1{,}113704,\\{\frac {db_{\frac {1}{2}}^{(6)}}{d\alpha }}&=0{,}867147,&{\frac {db_{\frac {1}{2}}^{(7)}}{d\alpha }}&=0{,}668830\,;\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=7{,}719923,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=7{,}531096,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=8{,}558595,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=9{,}112527,&{\frac {d^{2}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{2}}}&=9{,}107400,&{\frac {d^{2}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{2}}}&=8{,}634030,\\{\frac {d^{2}b_{\frac {1}{2}}^{(6)}}{d\alpha ^{2}}}&=7{,}842733\,;&&&&\\\\{\frac {d^{3}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{3}}}&=56{,}55335,&{\frac {d^{3}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{3}}}&=57{,}35721,&{\frac {d^{3}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{3}}}&=58{,}19633,\\{\frac {d^{3}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{3}}}&=62{,}87646,&{\frac {d^{3}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{3}}}&=66{,}32409,&{\frac {d^{3}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{3}}}&=70{,}54326\,;\\\\b_{\frac {3}{2}}^{(0)}&=9{,}992539,&b_{\frac {3}{2}}^{(1)}&=8{,}871894,&b_{\frac {3}{2}}^{(2)}&=7{,}386580,\\b_{\frac {3}{2}}^{(3)}&=5{,}953940,&b_{\frac {3}{2}}^{(4)}&=4{,}704321,&b_{\frac {3}{2}}^{(5)}&=3{,}652052\,;\\\\\end{alignedat}}$

${\frac {db_{\frac {3}{2}}^{(3)}}{d\alpha }}=56{,}65440,\qquad {\frac {db_{\frac {3}{2}}^{(4)}}{d\alpha }}=50{,}90290.$