be an even function. Then we will consider the exponential weights
in the weight class from E. Levin
and D. S. Lubinsky
[Orthogonal polynomials for exponential weights, Springer, New York (2001; Zbl 0997.42011
)]. In the paper, we will give some relations among exponential weights in this class and introduce a new weight subclass. In addition, we will investigate some properties of the typical and specific weights in these weight classes.