let′s define linear differantial operator D as D=z∙((d )/dz)(z∙((d )/dz))+z(1−((α/z))^2 ) when Df(z)={z∙((d )/dz)(z∙((d )/dz))+z(1−((α/z))^2 )}f(z)=0 f(z)=?


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Question Number 214667 by issac last updated on 16/Dec/24
$let′s define linear differantial operator D as D=z∙((d )/dz)(z∙((d )/dz))+z(1−((α/z))^2 ) when Df(z)={z∙((d )/dz)(z∙((d )/dz))+z(1−((α/z))^2 )}f(z)=0 f(z)=?$
${let}^{'} s define linear differantial operator D$ $as D = z \cdot \frac{d}{d z} (z \cdot \frac{d}{d z}) + z (1 - {(\frac{α}{z})}^{2})$ $when$ $D f (z) = {z \cdot \frac{d}{d z} (z \cdot \frac{d}{d z}) + z (1 - {(\frac{α}{z})}^{2})} f (z) = 0$ $f (z) = ?$
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