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DLMF:28.8#Ex4 - MaRDI portal

DLMF:28.8#Ex4 (Q8967)

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DLMF:28.8#Ex4
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    DLMF defining formula
    se m + 1 ⁡ ( x , h 2 ) se m + 1 ′ ⁡ ( 0 , h 2 ) = 2 m - ( 1 / 2 ) τ m + 1 ⁢ ( W m + ⁢ ( x ) ⁢ ( P m ⁢ ( x ) - Q m ⁢ ( x ) ) - W m - ⁢ ( x ) ⁢ ( P m ⁢ ( x ) + Q m ⁢ ( x ) ) ) , Mathieu-se 𝑚 1 𝑥 superscript ℎ 2 diffop Mathieu-se 𝑚 1 1 0 superscript ℎ 2 superscript 2 𝑚 1 2 subscript 𝜏 𝑚 1 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{se}_{m+1}\left(x,h^{2}\right)}{% \mathrm{se}_{m+1}'\left(0,h^{2}\right)}=\dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1% }}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)% ,}}
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