Formula:8978

Digital Library of Mathematical Functions ID 28.10.E6

${\displaystyle{\displaystyle\frac{2}{\pi}\int_{0}^{\ifrac{\pi}{2}}\sin z\sin t\cos\left(2h\cos z\cos t\right)\mathrm{se}_{2n+1}\left(t,h^{2}\right)\mathrm{d}t=\frac{B_{1}^{2n+1}(h^{2})}{2\mathrm{se}_{2n+1}\left(\frac{1}{2}\pi,h^{2}\right)}\mathrm{se}_{2n+1}\left(z,h^{2}\right),}}$

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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