By the Cauchy-Kowalewski extensions and Cauchy-Kowalewski product for the Octonionic valued functions,two extension theorems are obtained in Octonionic analysis.

By the Cauchy-Kowalewski extensions and Cauchy-Kowalewski product for the Octonionic valued functions,two extension theorems are obtained in Octonionic analysis.

Theoretical proof based on the impedance model and Cauchy integral formula was presented,emulation was performed on various experimental data to verify and illustrate the proposition.

With various methods to prove the fundamental theorem of algebra analyzed, this paper use the elementary method, Cauchy integral theorem and the theorem of Brouwer s immovable point to prove the fundamental theorem of Algebra.

Then the corresponding formal solution of this problem is also presented to be so-called Cauchy type integral,whose density function is an unique solution of a class of periodic Fredholm type equation.

The Cauchy type integral and Hlder continuity are studied.

Using the Cauchy type integral of bianalytic functions and the singular integral equation method, we have not only establishep an explicit form the general solutions of the Haseman problems for bianalytic functions, but also found the conditions for the solvability of the above problem.

Taylor coefficients and multipliers of Cauchy-Stieltjes integrals;

Some properties of Cauchy-Stieltjes integrals and their multipliers on the n-dimensional complex space are studied .

We consider the function space Fα consisting of Cauchy-Stieltjes integrals.