- #1
dobry_den
- 115
- 0
[tex]\biggl(-\frac{x^2}2 + \frac{x^4}{24} - \frac{x^6}{720} +\mathcal{O}(x^8)\biggr)-\frac12\biggl(-\frac{x^2}2+\frac{x^4}{24}+\mathcal{O}(x^6)\biggr)^2+\frac13\biggl(-\frac{x^2}2+\mathcal{O}(x^4)\biggr)^3 + \mathcal{O}(x^8)\\ & =-\frac{x^2}2 + \frac{x^4}{24}-\frac{x^6}{720} - \frac{x^4}8 + \frac{x^6}{48} - \frac{x^6}{24} +\mathcal{O}(x^8)\\
[/tex]
(http://en.wikipedia.org/wiki/Taylor_series#First_example)
This is a Taylor expansion of f(x) = ln(cos(x)) . I just wonder what happened with the first three O's, especially with (O(x^6))^2 and (O(x^4))^3. Are they somehow incorporated in O(x^8)?
[/tex]
(http://en.wikipedia.org/wiki/Taylor_series#First_example)
This is a Taylor expansion of f(x) = ln(cos(x)) . I just wonder what happened with the first three O's, especially with (O(x^6))^2 and (O(x^4))^3. Are they somehow incorporated in O(x^8)?