Formula:8979

Digital Library of Mathematical Functions ID 28.10.E7

${\displaystyle{\displaystyle\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin z\sin t\sin\left(2h\cos z\cos t\right)\mathrm{se}_{2n+2}\left(t,h^{2}\right)\mathrm{d}t=-\frac{hB_{2}^{2n+2}(h^{2})}{2\mathrm{se}_{2n+2}'\left(\frac{1}{2}\pi,h^{2}\right)}\mathrm{se}_{2n+2}\left(z,h^{2}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle B_{m}(q)}}$: Fourier coefficient
 

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