let-D-D-0-1-and-f-z-n-0-a-n-z-n-is-a-holomorphe-function-f-x-lt-1-1-z-prove-that-a-n-n-1-1-1-n-n-n-1-e-

Question Number 37294 by math khazana by abdo last updated on 11/Jun/18

l e t D = D (0, 1) a n d f (z) = \sum_{n = 0}^{\infty} a_{n} z^{n} i s a h o l o m o r p h e

f u n c t i o n / ∣ f (x) ∣< \frac{1}{1 - ∣ z ∣} p r o v e t h a t

∣ a_{n} ∣⩽ (n + 1) {(1 + \frac{1}{n})}^{n} ⩽ (n + 1) e .