About Equation HACS.2.2.1.1 |
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LaTeX encoding |
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\operatorname{arccosh} (x)\approx \sqrt{x - 1} \Biggl(\sqrt{2} - \frac{\sqrt{2} (x - 1)}{12} + \frac{3 \sqrt{2} (x - 1)^{2}}{160} - \\
\quad{}\quad{}\frac{5 \sqrt{2} (x - 1)^{3}}{896} + \frac{35 \sqrt{2} (x - 1)^{4}}{18432} - \frac{63 \sqrt{2} (x - 1)^{5}}{90112} + \\
\quad{}\quad{}\frac{231 \sqrt{2} (x - 1)^{6}}{851968} - \frac{143 \sqrt{2} (x - 1)^{7}}{1310720} + \frac{6435 \sqrt{2} (x - 1)^{8}}{142606336} - \\
\quad{}\quad{}\frac{12155 \sqrt{2} (x - 1)^{9}}{637534208} + \frac{46189 \sqrt{2} (x - 1)^{10}}{5637144576} - \frac{88179 \sqrt{2} (x - 1)^{11}}{24696061952} \\
\quad{}\quad{}+ \frac{676039 \sqrt{2} (x - 1)^{12}}{429496729600} - \frac{1300075 \sqrt{2} (x - 1)^{13}}{1855425871872} + \\
\quad{}\quad{}\frac{5014575 \sqrt{2} (x - 1)^{14}}{15942918602752} - \frac{9694845 \sqrt{2} (x - 1)^{15}}{68169720922112}\ldots\Biggr)
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`&sepsequence`(`¬hing`,`&operatorname`(arccosh)(x),approx,nullspace,(x-1)^(1/2)*`&delimiter`(leftparens,rightparens,false,`&sepsequence`(`¬hing`,2^(1/2)-1/12*2^(1/2)*(x-1)+3/160*2^(1/2)*(x-1)^2-5/896*2^(1/2)*(x-1)^3+35/18432*2^(1/2)*(x-1)^4-63/90112*2^(1/2)*(x-1)^5+231/851968*2^(1/2)*(x-1)^6-143/1310720*2^(1/2)*(x-1)^7+6435/142606336*2^(1/2)*(x-1)^8-12155/637534208*2^(1/2)*(x-1)^9+46189/5637144576*2^(1/2)*(x-1)^10-88179/24696061952*2^(1/2)*(x-1)^11+676039/429496729600*2^(1/2)*(x-1)^12-1300075/1855425871872*2^(1/2)*(x-1)^13+5014575/15942918602752*2^(1/2)*(x-1)^14-9694845/68169720922112*2^(1/2)*(x-1)^15,ldots)))