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We generalise the classical Bernstein's inequality: 
. Moreover we obtain a new representation formula for entire functions of exponential type.
Let R > 1 and denote by ℰR the ellipse
(1)
If Pn is a polynomial of degree at most n such that
(2)
then ([2]; also see [13, p. 337] and [9, p. 158, Prob. No. 270])
(3)
The standard proof of this well known result runs as follows. The function
(4)
is entire and in view of (2) we have
Hence by the maximum modulus principle
(5)
which is clearly equivalent to (3).
