Category:Power Series Expansion for Secant Function
Jump to navigation
Jump to search
This category contains pages concerning Power Series Expansion for Secant Function:
The (real) secant function has a Taylor series expansion:
| \(\ds \sec x\) | \(=\) | \(\ds \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {E_{2 n} x^{2 n} } {\paren {2 n}!}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1 + \frac {x^2} 2 + \frac {5 x^4} {24} + \frac {61 x^6} {720} + \dfrac {1385 x^8} {40320} + \cdots\) |
where $E_{2 n}$ denotes the Euler numbers.
This converges for $\size x < \dfrac \pi 2$.
Pages in category "Power Series Expansion for Secant Function"
The following 2 pages are in this category, out of 2 total.