DLMF:28.28.E44 (Q8475)

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DLMF:28.28.E44
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    1 π 2 0 2 π sin ( 2 t ) se n ( t , h 2 ) ce m ( t , h 2 ) sinh 2 z + sin 2 t d t = ( - 1 ) p i γ ^ n , m Dsc 0 ( n , m , z ) , 1 superscript 𝜋 2 superscript subscript 0 2 𝜋 2 𝑡 Mathieu-se 𝑛 𝑡 superscript 2 Mathieu-ce 𝑚 𝑡 superscript 2 2 𝑧 2 𝑡 𝑡 superscript 1 𝑝 imaginary-unit subscript ^ 𝛾 𝑛 𝑚 Mathieu-Dsc 0 𝑛 𝑚 𝑧 {\displaystyle{\displaystyle\dfrac{1}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\sin\left(% 2t\right)\mathrm{se}_{n}\left(t,h^{2}\right)\mathrm{ce}_{m}\left(t,h^{2}\right% )}{{\sinh^{2}}z+{\sin^{2}}t}\mathrm{d}t=(-1)^{p}\mathrm{i}\widehat{\gamma}_{n,% m}\mathrm{Dsc}_{0}\left(n,m,z\right),}}
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