DLMF:24.7.E10 (Q7486)

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DLMF:24.7.E10
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    Defining formula
    E 2 ⁢ n + 1 ⁡ ( x ) = ( - 1 ) n + 1 ⁢ 4 ⁢ ∫ 0 ∞ cos ⁡ ( π ⁢ x ) ⁢ sinh ⁡ ( π ⁢ t ) cosh ⁡ ( 2 ⁢ π ⁢ t ) - cos ⁡ ( 2 ⁢ π ⁢ x ) ⁢ t 2 ⁢ n + 1 ⁢ d t . Euler-polynomial-E 2 𝑛 1 𝑥 superscript 1 𝑛 1 4 superscript subscript 0 𝜋 𝑥 𝜋 𝑡 2 𝜋 𝑡 2 𝜋 𝑥 superscript 𝑡 2 𝑛 1 𝑡 {\displaystyle{\displaystyle E_{2n+1}\left(x\right)=(-1)^{n+1}4\*\int_{0}^{% \infty}\frac{\cos\left(\pi x\right)\sinh\left(\pi t\right)}{\cosh\left(2\pi t% \right)-\cos\left(2\pi x\right)}t^{2n+1}\mathrm{d}t.}}
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    DLMF id
    DLMF:24.7.E10
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