定義：對(duì)任意復(fù)數(shù)x，Euler數(shù)[latex]E_{2n}(n=0,1,2,\cdots)[/latex]由下式給出：

[latex]\sec x=\sum\limits_{n=0}^{+\infty}(-1)^nE_{2n}\frac{x^{2n}}{(2n)!},\quad\mid x\mid<\frac{\pi}{2}[/latex]

[latex]E_0=1,\quad\sum\limits_{k=0}^n\left(\begin{array}{l}2n\\2k\end{array}\right)E_{2k}=0(n\geqslant 1)[/latex]

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