Let n be a positive integer and [C.sup.n] denote the space of n

complex variables z = ([z.sub.1],..., [z.sub.n]) with the Euclidean inner product [??]z,w[??] = [n.summation over (j=1)] [z.sub.j][bar.w.sub.j] and Euclidean norm ||z|| = [(z, z).sup.1/2], where z, w [member of] [C.sup.n].

The third HP transfer function considered in this work applies the traditional substitution of the

complex variable s by 1/s.

We consider [B.sub.z](a, b) as a function of the

complex variable z and derive new convergent expansions that are uniformly valid in an unbounded region of the complex z-plane that contains the point z = 0.

Kassab, "

Complex variable boundary element methods for the solution of potential problems in simply and multiply connected domains," Computer Methods Applied Mechanics and Engineering, vol.

The

complex variable derivation method is used to calculate the matrix of sensitivity coefficient.

So the Roper-Suffridge operator plays an important role in several

complex variables. In recent years, there are lots of results about the Roper-Suffridge extension operator which was generalized and modified on different domains in different spaces to preserve the geometric characteristics of convex mappings, star-like mappings, and their subclasses.

In theory of basic sets of polynomials in hypercomplex analysis, Abul-Ez and Constales gave in [21,22] the extension of the theory of bases of polynomials in one

complex variable to the setting of Clifford analysis.

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the component which has negative poles of the

complex variable j[omega] and can be realized physically, [{[S.sub.[bar.M]]([omega])/[psi](-j[omega])}.sup.-] is the component which has positive poles of the

complex variable j[omega] and can not be realized physically.

This algorithm should be based on boundary integral equations method and apparatus of the

complex variable theory.

Thanks to its innovative design, it offers the versatility to create extensive and innovative applications across a wide range of media, including heavyweight coated stocks and envelopes, and can flexibly handle everything from short runs to

complex variable data printing for personalised print communications.

This ensures that process parameters are fully understood across what is typically a

complex variable space, reducing risk and providing a robust and reliable scientific approach to process validation.

The use of the Fourier (Brekhovskikh, Goncharov 1982) or Laplace (Lavrentyev, Shabat 1973) transformation methods (applying a function of a

complex variable) provides the possibility to present the solutions to boundary-value problems in simple series in terms of eigenvalues and to extend them to the cases of non-stationary wave processes.