Effective analytic functions

Effective analytic functions

One approach for computations with special functions in computer algebra is the systematic use of analytic functions whenever possible. This naturally leads to problems of how to answer questions about analytic functions in a fully eeective way. Such questions comprise the determination of the radius of convergence or the evaluation of the analytic continuation of the function at the endpoint o...

A Subclass of Analytic Functions Associated with Hypergeometric Functions

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

On Effective Analytic Continuation

Until now, the area of symbolic computation has mainly focused on the manipulation of algebraic expressions. It would be interesting to apply a similar spirit of “exact computations” to the field of mathematical analysis. One important step for such a project is the ability to compute with computable complex numbers and computable analytic functions. Such computations include effective analytic...

Quasi-analytic Vectors and Quasi-analytic Functions

Bounded Analytic Functions

If D is a domain in the complex s-plane, then the family B=B(D) of bounded analytic functions in D is defined as consisting of those analytic functions ƒ(z) which are regular and single-valued in D and which satisfy the inequality \f(z) | < 1 at all points of D. The classical investigations of the family B(D) were restricted to the case in which D is a simply-connected domain. In fact, D was ge...