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DLMF:28.8#Ex3 - MaRDI portal

DLMF:28.8#Ex3 (Q8966)

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DLMF:28.8#Ex3
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    DLMF defining formula
    ce m ⁡ ( x , h 2 ) ce m ⁡ ( 0 , h 2 ) = 2 m - ( 1 / 2 ) σ m ⁢ ( W m + ⁢ ( x ) ⁢ ( P m ⁢ ( x ) - Q m ⁢ ( x ) ) + W m - ⁢ ( x ) ⁢ ( P m ⁢ ( x ) + Q m ⁢ ( x ) ) ) , Mathieu-ce 𝑚 𝑥 superscript ℎ 2 Mathieu-ce 𝑚 0 superscript ℎ 2 superscript 2 𝑚 1 2 subscript 𝜎 𝑚 superscript subscript 𝑊 𝑚 𝑥 subscript 𝑃 𝑚 𝑥 subscript 𝑄 𝑚 𝑥 superscript subscript 𝑊 𝑚 𝑥 subscript 𝑃 𝑚 𝑥 subscript 𝑄 𝑚 𝑥 {\displaystyle{\displaystyle\dfrac{\mathrm{ce}_{m}\left(x,h^{2}\right)}{% \mathrm{ce}_{m}\left(0,h^{2}\right)}=\dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}% \left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right),}}
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