In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

We present an operator approach to Rogers-type formulas and Mehler’s formulas for the Al-Salam-Carlitz polynomials Un(x, y, a; q). By using the q-exponential operator, we obtain a Rogers-type formula which leads to a linearization formula. With the aid of a bivariate augmentation operator, we get a simple derivation of Mehler’s formula due to AlSalam and Carlitz. By means of the Cauchy companio...

This paper considers a variety of parity questions connected with classical partition identities of Euler, Rogers, Ramanujan and Gordon. We begin by restricting the partitions in the Rogers-Ramanujan-Gordon identities to those wherein even parts appear an even number of times. We then take up questions involving sequences of alternating parity in the parts of partitions. This latter study leads...

We reexamine Alan R. Rogers’ (1994) analysis of the biological basis of the rate of time preference. Although his basic insight concerning the derivation of the utility function holds up, the functional form he uses does not generate equilibrium evolutionary behavior. Moreover, Rogers relies upon an interior solution for a particular kind of intergenerational transfer. We show such interior sol...