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 \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) = ?