The real part of a complex number is referenced on the horizontal real axis of the

complex plane and the imaginary part is referenced on the vertical imaginary axis.

Let a and b be two distinct finite values, and let f be a meromorphic function in the

complex plane such that f has finitely many poles in the

complex plane.

For doing that, the first step is matching the original image coordinates with a

complex plane; in this case it was used the upper-right region of the

complex plane, where the real and the imaginary coordinates are positive.

We will consider this problems for algebraic polynomials of complex variables in the well known Bergman space, and investigate the following problems: evaluating the increase of the modulus of polynomials in the exterior of the given region with respect to the norm of the polynomial in the this region; determining a change of (semi)norm of polynomials for the given region and, finally, combining obtained estimations for the modulus of polynomials, we will get the estimation modulus of polynomials in whole

complex plane.

As can be seen the origin of the

complex plane is excluded from the value sets and thus the family (5) is robustly stable.

z) are analytic in the complete

complex plane cut along the sections [L.

To preserve a certain degree of stability, the migration of poles should be strictly limited in the left half-plane of the

complex plane.

In this example the feasible region is a surface in the

complex plane.

With rectangular representation, a rectangle is constructed in the

complex plane.

Shimomura Painleve Differential Equations in the

Complex Plane, Walter de Gruyter, New York, NY, USA.

In this paper we investigate the so-called extended eigenvalues and extended eigenvectors and cyclicity problems for some convolution operators acting on the space of analytic functions defined on the starlike domain D of the

complex plane.

This is usually achieved setting up a search in the

complex plane which can be time consuming if an adequate starting point is not available.