DLMF:28.28.E47 (Q8478)

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DLMF:28.28.E47
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    sinh z π 2 0 2 π cos t ce n ( t , h 2 ) ce m ( t , h 2 ) sinh 2 z + sin 2 t d t = ( - 1 ) p + 1 i h α ^ n , m ( c ) Dc 0 ( n , m , z ) , 𝑧 superscript 𝜋 2 superscript subscript 0 2 𝜋 𝑡 Mathieu-ce 𝑛 𝑡 superscript 2 Mathieu-ce 𝑚 𝑡 superscript 2 2 𝑧 2 𝑡 𝑡 superscript 1 𝑝 1 imaginary-unit superscript subscript ^ 𝛼 𝑛 𝑚 𝑐 Mathieu-Dc 0 𝑛 𝑚 𝑧 {\displaystyle{\displaystyle\dfrac{\sinh z}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\cos t% \mathrm{ce}_{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{\alpha}_{n,m}^{(c% )}\mathrm{Dc}_{0}\left(n,m,z\right),}}
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    DLMF:28.28.E47
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