Formula:9138

Digital Library of Mathematical Functions ID 28.28.E20

${\displaystyle{\displaystyle\dfrac{2}{\pi}\int_{0}^{\pi}\mathcal{C}^{(j)}_{2\ell}(2hR)\cos\left(2\ell\phi\right)\mathrm{ce}_{2m}\left(t,h^{2}\right)\mathrm{d}t=\varepsilon_{\ell}(-1)^{\ell+m}A^{2m}_{2\ell}(h^{2}){\mathrm{Mc}^{(j)}_{2m}}\left(z,h\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$:
• ${\displaystyle{\displaystyle\pi}}$: 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
• ${\displaystyle{\displaystyle{\mathrm{Mc}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z},\NVar{h}\right)}}$: radial Mathieu function
• ${\displaystyle{\displaystyle m}}$: integer
• ${\displaystyle{\displaystyle h}}$: parameter
• ${\displaystyle{\displaystyle j}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\mathcal{C}_{\mu}^{(j)}}}$: cylinder functions
• ${\displaystyle{\displaystyle\phi(z,t)}}$: function
• ${\displaystyle{\displaystyle R(z,t)}}$: function
• ${\displaystyle{\displaystyle\varepsilon_{\ell}}}$: constants
• ${\displaystyle{\displaystyle A_{m}(q)}}$: Fourier coefficient
 

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