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DLMF:28.20#Ex6 - MaRDI portal

DLMF:28.20#Ex6 (Q9049)

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DLMF:28.20#Ex6
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    𝒲 { M ν ( 1 ) , M ν ( 3 ) } = - 𝒲 { M ν ( 1 ) , M ν ( 4 ) } = - 1 2 𝒲 { M ν ( 3 ) , M ν ( 4 ) } = 2 i / π . Wronskian modified-Mathieu-M 1 𝜈 modified-Mathieu-M 3 𝜈 Wronskian modified-Mathieu-M 1 𝜈 modified-Mathieu-M 4 𝜈 1 2 Wronskian modified-Mathieu-M 3 𝜈 modified-Mathieu-M 4 𝜈 2 imaginary-unit 𝜋 {\displaystyle{\displaystyle\mathscr{W}\left\{{\mathrm{M}^{(1)}_{\nu}},{% \mathrm{M}^{(3)}_{\nu}}\right\}=-\mathscr{W}\left\{{\mathrm{M}^{(1)}_{\nu}},{% \mathrm{M}^{(4)}_{\nu}}\right\}={-\tfrac{1}{2}\mathscr{W}\left\{{\mathrm{M}^{(% 3)}_{\nu}},{\mathrm{M}^{(4)}_{\nu}}\right\}=\ifrac{2\mathrm{i}}{\pi}}.}}
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