Result: Taylor series and orthogonality of the Octonion analytic functions: Taylor series and orthogonality of the octonion analytic functions

Hypercomplex function theories, especially quaternionic analysis and Clifford analysis, and their successful application to partial differential equations during the last decades have led the authors to the investigation of the alternative division algebra of Cayley's octonions. Aiming at the development of an octonion analysis, they have already obtained several results within the last years. In the present paper, a Taylor type theorem and related theorems are obtained, e.g., for a left octonion analytic (``0-analytic'') function a series development is stated by means of left spherical 0-analytic functions. Moreover, the orthogonal formula for 0-analytic functions is proved by use of a suitable form of the Stokes theorem.