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DLMF:10.63#Ex7 - MaRDI portal

DLMF:10.63#Ex7 (Q4511)

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DLMF:10.63#Ex7
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    f ν ( x ) = - ( 1 / 2 ) ( f ν - 1 ( x ) + g ν - 1 ( x ) ) - ( ν / x ) f ν ( x ) , superscript subscript 𝑓 𝜈 𝑥 1 2 subscript 𝑓 𝜈 1 𝑥 subscript 𝑔 𝜈 1 𝑥 𝜈 𝑥 subscript 𝑓 𝜈 𝑥 {\displaystyle{\displaystyle f_{\nu}^{\prime}(x)=-(1/\sqrt{2})\left(f_{\nu-1}(% x)+g_{\nu-1}(x)\right)-(\nu/x)f_{\nu}(x),}}
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