DLMF:28.23.E4 (Q8388)

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DLMF:28.23.E4
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    me ν ( 1 2 π , h 2 ) M ν ( j ) ( z , h ) = e i ν π / 2 n = - c 2 n ν ( h 2 ) 𝒞 ν + 2 n ( j ) ( 2 h sinh z ) , Mathieu-me 𝜈 1 2 𝜋 superscript 2 modified-Mathieu-M 𝑗 𝜈 𝑧 superscript 𝑒 imaginary-unit 𝜈 𝜋 2 superscript subscript 𝑛 superscript subscript 𝑐 2 𝑛 𝜈 superscript 2 superscript subscript 𝒞 𝜈 2 𝑛 𝑗 2 𝑧 {\displaystyle{\displaystyle\mathrm{me}_{\nu}\left(\tfrac{1}{2}\pi,h^{2}\right% ){\mathrm{M}^{(j)}_{\nu}}\left(z,h\right)=e^{\mathrm{i}\nu\ifrac{\pi}{2}}\sum_% {n=-\infty}^{\infty}c_{2n}^{\nu}(h^{2}){\cal C}_{\nu+2n}^{(j)}(2h\sinh z),}}
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    DLMF:28.23.E4
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