DLMF:28.24.E2 (Q8399)

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DLMF:28.24.E2
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    ε s Mc 2 m ( j ) ( z , h ) = ( - 1 ) m = 0 ( - 1 ) A 2 2 m ( h 2 ) A 2 s 2 m ( h 2 ) ( J - s ( h e - z ) 𝒞 + s ( j ) ( h e z ) + J + s ( h e - z ) 𝒞 - s ( j ) ( h e z ) ) , subscript 𝜀 𝑠 modified-Mathieu-Mc 𝑗 2 𝑚 𝑧 superscript 1 𝑚 superscript subscript 0 superscript 1 superscript subscript 𝐴 2 2 𝑚 superscript 2 superscript subscript 𝐴 2 𝑠 2 𝑚 superscript 2 Bessel-J 𝑠 superscript 𝑒 𝑧 superscript subscript 𝒞 𝑠 𝑗 superscript 𝑒 𝑧 Bessel-J 𝑠 superscript 𝑒 𝑧 superscript subscript 𝒞 𝑠 𝑗 superscript 𝑒 𝑧 {\displaystyle{\displaystyle\varepsilon_{s}{\mathrm{Mc}^{(j)}_{2m}}\left(z,h% \right)=(-1)^{m}\sum_{\ell=0}^{\infty}(-1)^{\ell}\frac{A_{2\ell}^{2m}(h^{2})}{% A_{2s}^{2m}(h^{2})}\left(J_{\ell-s}\left(he^{-z}\right){\cal C}_{\ell+s}^{(j)}% (he^{z})+J_{\ell+s}\left(he^{-z}\right){\cal C}_{\ell-s}^{(j)}(he^{z})\right),}}
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    DLMF:28.24.E2
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