Formula:9132

Digital Library of Mathematical Functions ID 28.28.E16

${\displaystyle{\displaystyle\int_{0}^{\infty}\sin\left(2h\cos y\cosh t\right)\mathrm{Ce}_{2n}\left(t,h^{2}\right)\mathrm{d}t=-\dfrac{\pi A_{0}^{2n}(h^{2})}{2\mathrm{ce}_{2n}\left(\frac{1}{2}\pi,h^{2}\right)}\*\left(\mathrm{ce}_{2n}\left(y,h^{2}\right)\mp\dfrac{2}{\pi C_{2n}(h^{2})}\mathrm{fe}_{2n}\left(y,h^{2}\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{fe}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$: second solution, Mathieu’s equation
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathrm{Ce}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}\right)}}$: modified Mathieu function
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle A_{m}(q)}}$: Fourier coefficient
• ${\displaystyle{\displaystyle C_{n}(q)}}$: factor
 

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