About Equation ACS.2.2.1.1
top up back next into bottom


\begin{equation*} 
\begin{split} 
& \operatorname{arccos} (x)\approx \sqrt{x - 1} \biggl(-\frac{5 i}{896}\sqrt{2} (x - 1)^{3} + \frac{231 i}{851968} \sqrt{2} (x - 1)^{6} -  \\ 
& \quad{}\quad{}\frac{9694845 i}{68169720922112} \sqrt{2} (x - 1)^{15} + i \sqrt{2} +  \\ 
& \quad{}\quad{}\frac{46189 i}{5637144576} \sqrt{2} (x - 1)^{10} - \frac{1300075 i}{1855425871872} \sqrt{2} (x - 1)^{13} +  \\ 
& \quad{}\quad{}\frac{6435 i}{142606336} \sqrt{2} (x - 1)^{8} - \frac{143 i}{1310720} \sqrt{2} (x - 1)^{7} +  \\ 
& \quad{}\quad{}\frac{35 i}{18432} \sqrt{2} (x - 1)^{4} + \frac{5014575 i}{15942918602752} \sqrt{2} (x - 1)^{14} -  \\ 
& \quad{}\quad{}\frac{88179 i}{24696061952} \sqrt{2} (x - 1)^{11} - \frac{i}{12} \sqrt{2} (x - 1) + \frac{3 i}{160} \sqrt{2} (x - 1)^{2} -  \\ 
& \quad{}\quad{}\frac{63 i}{90112} \sqrt{2} (x - 1)^{5} - \frac{12155 i}{637534208} \sqrt{2} (x - 1)^{9} +  \\ 
& \quad{}\quad{}\frac{676039 i}{429496729600} \sqrt{2} (x - 1)^{12}\ldots\biggr) 
\end{split} 
\end{equation*}
Absolute reference: ACS:asympt:1:terms
LaTeX encoding
top up back next into bottom
\operatorname{arccos} (x)\approx \sqrt{x - 1} \biggl(-\frac{5 i}{896}\sqrt{2} (x - 1)^{3} + \frac{231 i}{851968} \sqrt{2} (x - 1)^{6} - \\ \quad{}\quad{}\frac{9694845 i}{68169720922112} \sqrt{2} (x - 1)^{15} + i \sqrt{2} + \\ \quad{}\quad{}\frac{46189 i}{5637144576} \sqrt{2} (x - 1)^{10} - \frac{1300075 i}{1855425871872} \sqrt{2} (x - 1)^{13} + \\ \quad{}\quad{}\frac{6435 i}{142606336} \sqrt{2} (x - 1)^{8} - \frac{143 i}{1310720} \sqrt{2} (x - 1)^{7} + \\ \quad{}\quad{}\frac{35 i}{18432} \sqrt{2} (x - 1)^{4} + \frac{5014575 i}{15942918602752} \sqrt{2} (x - 1)^{14} - \\ \quad{}\quad{}\frac{88179 i}{24696061952} \sqrt{2} (x - 1)^{11} - \frac{i}{12} \sqrt{2} (x - 1) + \frac{3 i}{160} \sqrt{2} (x - 1)^{2} - \\ \quad{}\quad{}\frac{63 i}{90112} \sqrt{2} (x - 1)^{5} - \frac{12155 i}{637534208} \sqrt{2} (x - 1)^{9} + \\ \quad{}\quad{}\frac{676039 i}{429496729600} \sqrt{2} (x - 1)^{12}\ldots\biggr)
Maple encoding
top up back next into bottom
`&sepsequence`(`&nothing`,`&operatorname`(arccos)(x),approx,nullspace,(x-1)^(1/2)*`&delimiter`(leftparens,rightparens,false,`&sepsequence`(`&nothing`,-5/896*I*2^(1/2)*(x-1)^3+231/851968*I*2^(1/2)*(x-1)^6-9694845/68169720922112*I*2^(1/2)*(x-1)^15+I*2^(1/2)+46189/5637144576*I*2^(1/2)*(x-1)^10-1300075/1855425871872*I*2^(1/2)*(x-1)^13+6435/142606336*I*2^(1/2)*(x-1)^8-143/1310720*I*2^(1/2)*(x-1)^7+35/18432*I*2^(1/2)*(x-1)^4+5014575/15942918602752*I*2^(1/2)*(x-1)^14-88179/24696061952*I*2^(1/2)*(x-1)^11-1/12*I*2^(1/2)*(x-1)+3/160*I*2^(1/2)*(x-1)^2-63/90112*I*2^(1/2)*(x-1)^5-12155/637534208*I*2^(1/2)*(x-1)^9+676039/429496729600*I*2^(1/2)*(x-1)^12,ldots)))
 
 
 
This web site is compliant with HTML 4.01 and CSS 1.
Copyright © 2001-2003 by the Algorithms Project and INRIA.
All rights reserved. Created: Aug 1 2003 15:07:58.