DLMF:28.10.E7 (Q8286)

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DLMF:28.10.E7
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    2 π ⁢ ∫ 0 π / 2 sin ⁡ z ⁢ sin ⁡ t ⁢ sin ⁡ ( 2 ⁢ h ⁢ cos ⁡ z ⁢ cos ⁡ t ) ⁢ se 2 ⁢ n + 2 ⁡ ( t , h 2 ) ⁢ d t = - h ⁢ B 2 2 ⁢ n + 2 ⁢ ( h 2 ) 2 ⁢ se 2 ⁢ n + 2 ′ ⁡ ( 1 2 ⁢ π , h 2 ) ⁢ se 2 ⁢ n + 2 ⁡ ( z , h 2 ) , 2 𝜋 superscript subscript 0 𝜋 2 𝑧 𝑡 2 ℎ 𝑧 𝑡 Mathieu-se 2 𝑛 2 𝑡 superscript ℎ 2 𝑡 ℎ superscript subscript 𝐵 2 2 𝑛 2 superscript ℎ 2 2 diffop Mathieu-se 2 𝑛 2 1 1 2 𝜋 superscript ℎ 2 Mathieu-se 2 𝑛 2 𝑧 superscript ℎ 2 {\displaystyle{\displaystyle\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin z\sin t% \sin\left(2h\cos z\cos t\right)\mathrm{se}_{2n+2}\left(t,h^{2}\right)\mathrm{d% }t=-\frac{hB_{2}^{2n+2}(h^{2})}{2\mathrm{se}_{2n+2}'\left(\frac{1}{2}\pi,h^{2}% \right)}\mathrm{se}_{2n+2}\left(z,h^{2}\right),}}
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    DLMF:28.10.E7
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