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Question Number 214667 by issac last updated on 15/Dec/24

$${\mathrm{let}}^{\prime }\mathrm{s}\mathrm{define}\mathrm{linear}\mathrm{differantial}\mathrm{operator}\mathcal{D}$$$$\mathrm{as}\mathcal{D}=z\cdot \frac{\mathrm{d}}{\mathrm{d}z}\left(z\frac{\mathrm{d}}{\mathrm{d}z}\right)+z(1-{\left(\frac{\alpha }{z}\right)}^2)$$$$\mathrm{when}\mathcal{D}\ast f\left(z\right)=0$$$$f\left(z\right)=?$$

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