DLMF:28.28.E20 (Q8446)

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DLMF:28.28.E20
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    2 π 0 π 𝒞 2 ( j ) ( 2 h R ) cos ( 2 ϕ ) ce 2 m ( t , h 2 ) d t = ε ( - 1 ) + m A 2 2 m ( h 2 ) Mc 2 m ( j ) ( z , h ) , 2 𝜋 superscript subscript 0 𝜋 subscript superscript 𝒞 𝑗 2 2 𝑅 2 italic-ϕ Mathieu-ce 2 𝑚 𝑡 superscript 2 𝑡 subscript 𝜀 superscript 1 𝑚 subscript superscript 𝐴 2 𝑚 2 superscript 2 modified-Mathieu-Mc 𝑗 2 𝑚 𝑧 {\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),}}
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    DLMF:28.28.E20
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