DLMF:28.28.E41 (Q8472)

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DLMF:28.28.E41
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    cosh z π 2 0 2 π sin t se n ( t , h 2 ) ce m ( t , h 2 ) sinh 2 z + sin 2 t d t = ( - 1 ) p + 1 i h β ^ n , m Dsc 0 ( n , m , z ) , 𝑧 superscript 𝜋 2 superscript subscript 0 2 𝜋 𝑡 Mathieu-se 𝑛 𝑡 superscript 2 Mathieu-ce 𝑚 𝑡 superscript 2 2 𝑧 2 𝑡 𝑡 superscript 1 𝑝 1 imaginary-unit subscript ^ 𝛽 𝑛 𝑚 Mathieu-Dsc 0 𝑛 𝑚 𝑧 {\displaystyle{\displaystyle\dfrac{\cosh z}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\sin t% \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+1}\mathrm{i}h\widehat{\beta}_{n,m}% \mathrm{Dsc}_{0}\left(n,m,z\right),}}
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