Power series with multiply monotonic coefficients.

Power Series with Integral Coefficients

Let f(z) be a function, meromorphic in \z\ < 1 , whose power series around the origin has integral coefficients. In [5], Salem shows that if there exists a nonzero polynomial p(z) such that p(z)f(z) is in H, or else if there exists a complex number a, such that l/(f(z)—a) is bounded, when |JS| is close to 1, then f(z) is rational. In [2], Chamfy extends Salem's results by showing that if there ...

On Nilpotent Power Series with Nilpotent Coefficients

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto powerseries rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of...

Power-monotone Sequences and Fourier Series with Positive Coefficients

J. Németh has extended several basic theorems of R. P. Boas Jr. pertaining to Fourier series with positive coefficients from Lipschitz classes to generalized Lipschitz classes. The goal of the present work is to find the common root of known results of this type and to establish two theorems that are generalizations of Németh’s results. Our results can be considered as sample examples showing t...

Computer Algebra and Power Series with Positive Coefficients

We consider the question whether all the coefficients in the series expansions of some specific rational functions are positive, and we demonstrate how computer algebra can help answering questions arising in this context. By giving partial computer proofs, we provide new evidence in support of some longstanding open conjectures. Also two new conjectures are made.

On full rank differential systems with power series coefficients