DLMF:10.63#Ex8 (Q3815)

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DLMF:10.63#Ex8
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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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