DLMF:10.63#Ex5 (Q3812)

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DLMF:10.63#Ex5
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    f ν - 1 ( x ) + f ν + 1 ( x ) = - ( ν 2 / x ) ( f ν ( x ) - g ν ( x ) ) , subscript 𝑓 𝜈 1 𝑥 subscript 𝑓 𝜈 1 𝑥 𝜈 2 𝑥 subscript 𝑓 𝜈 𝑥 subscript 𝑔 𝜈 𝑥 {\displaystyle{\displaystyle f_{\nu-1}(x)+f_{\nu+1}(x)=-(\nu\sqrt{2}/x)\left(f% _{\nu}(x)-g_{\nu}(x)\right),}}
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