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DLMF:28.20#Ex12 - MaRDI portal

DLMF:28.20#Ex12 (Q9056)

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DLMF:28.20#Ex12
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    M ν ( 2 ) ( z + s π i , h ) = e - i s π ν M ν ( 2 ) ( z , h ) + 2 i cot ( π ν ) sin ( s π ν ) M ν ( 1 ) ( z , h ) , modified-Mathieu-M 2 𝜈 𝑧 𝑠 𝜋 imaginary-unit superscript 𝑒 imaginary-unit 𝑠 𝜋 𝜈 modified-Mathieu-M 2 𝜈 𝑧 2 imaginary-unit 𝜋 𝜈 𝑠 𝜋 𝜈 modified-Mathieu-M 1 𝜈 𝑧 {\displaystyle{\displaystyle{\mathrm{M}^{(2)}_{\nu}}\left(z+s\pi\mathrm{i},h% \right)=e^{-\mathrm{i}s\pi\nu}{\mathrm{M}^{(2)}_{\nu}}\left(z,h\right)+2% \mathrm{i}\cot\left(\pi\nu\right)\sin\left(s\pi\nu\right){\mathrm{M}^{(1)}_{% \nu}}\left(z,h\right),}}
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