Category:Power Series Expansion for Cosecant Function
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This category contains pages concerning Power Series Expansion for Cosecant Function:
The cosecant function has a Laurent series expansion:
| \(\ds \csc x\) | \(=\) | \(\ds \sum_{n \mathop = 0}^\infty \dfrac {\paren {-1}^{n - 1} 2 \paren {2^{2 n - 1} - 1} B_{2 n} \, x^{2 n - 1} } {\paren {2 n}!}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 1 x + \frac x 6 + \frac {7 x^3} {360} + \frac {31 x^5} {15 \, 120} + \cdots\) |
where $B_n$ denotes the Bernoulli numbers.
This converges for $0 < \size x < \pi$.
Pages in category "Power Series Expansion for Cosecant Function"
The following 2 pages are in this category, out of 2 total.