DLMF:28.28.E45 (Q8476)

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DLMF:28.28.E45
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    sinh ( 2 z ) π 2 0 2 π se n ( t , h 2 ) ce m ( t , h 2 ) sinh 2 z + sin 2 t d t = ( - 1 ) p + 1 i γ ^ n , m Dsc 1 ( n , m , z ) , 2 𝑧 superscript 𝜋 2 superscript subscript 0 2 𝜋 diffop Mathieu-se 𝑛 1 𝑡 superscript 2 Mathieu-ce 𝑚 𝑡 superscript 2 2 𝑧 2 𝑡 𝑡 superscript 1 𝑝 1 imaginary-unit subscript ^ 𝛾 𝑛 𝑚 Mathieu-Dsc 1 𝑛 𝑚 𝑧 {\displaystyle{\displaystyle\dfrac{\sinh\left(2z\right)}{\pi^{2}}\int_{0}^{2% \pi}\dfrac{\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}\widehat{% \gamma}_{n,m}\mathrm{Dsc}_{1}\left(n,m,z\right),}}
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