tag:
Euler_numbers
§
$$\frac{1}{{\cosh x}} = \sum\limits_{k = 0}^{ + \infty } {\frac{{{E_{2k}}{x^{2k}}}}{{\left( {2k} \right)!}}} ;$$
$$\frac{1}{{\cos x}} = \sum\limits_{k = 0}^{ + \infty } {\frac{{{{\left( { - 1} \right)}^k}{E_{2k}}{x^{2k}}}}{{\left( {2k} \right)!}}} ;$$
\[{E_{2k}}{\text{ - Euler numbers}}\]
2107.
$$\int\limits_0^{ + \infty } {\frac{{{x^{2n}}}}{{\cosh x}}dx} = \left| {{E_{2n}}} \right| \cdot {\left( {\frac{\pi }{2}} \right)^{2n + 1}},$$
\[n \in \mathbb{N}.\]