let-s-define-linear-differantial-operator-D-as-D-z-d-dz-z-d-dz-z-1-z-2-when-Df-z-z-d-dz-z-d-dz-z-1-z-2-f-z-0-f-z-

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)=?

$$\mathrm{let}'\mathrm{s}\:\mathrm{define}\:\mathrm{linear}\:\mathrm{differantial}\:\mathrm{operator}\:\mathcal{D} \\ $$$$\mathrm{as}\:\mathcal{D}={z}\centerdot\frac{\mathrm{d}\:\:}{\mathrm{d}{z}}\left({z}\centerdot\frac{\mathrm{d}\:\:}{\mathrm{d}{z}}\right)+{z}\left(\mathrm{1}−\left(\frac{\alpha}{{z}}\right)^{\mathrm{2}} \right) \\ $$$$\mathrm{when} \\ $$$$\mathcal{D}{f}\left({z}\right)=\left\{{z}\centerdot\frac{\mathrm{d}\:\:}{\mathrm{d}{z}}\left({z}\centerdot\frac{\mathrm{d}\:\:}{\mathrm{d}{z}}\right)+{z}\left(\mathrm{1}−\left(\frac{\alpha}{{z}}\right)^{\mathrm{2}} \right)\right\}{f}\left({z}\right)=\mathrm{0} \\ $$$${f}\left({z}\right)=? \\ $$

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let-s-define-linear-differantial-operator-D-as-D-z-d-dz-z-d-dz-z-1-z-2-when-Df-z-z-d-dz-z-d-dz-z-1-z-2-f-z-0-f-z-

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