Abstract:
Euler polynomials are named after mathematician Leonhard Euler (1707-
1783). These are the class of polynomials {En(x)} defined by
2e
xt
e
t + 1
=
X
∞
n=0
En(x)
t
n
n!
for |t| < π.
where the variables x and t can be real or complex and the integer
numbers En are called Euler number.
In this thesis, we mainly focus to this class of polynomials and review
properties of En(x). We establish an asymptotic behavior for En(x) and
determine their asymptotic zeros. We briefly explain the behavior of the
real and complex zeros of En(x) for sufficiently large positive integers n.
We pove for 0 ≤ x < 1 the asymptotic real zeros of En(x) approximately
given by:
x = 2k +
n
2
for some k ∈ Z.
