关键词: Polar coordinates, Taylor series, holomorphic functions

Abstract:

Some previous results on convergence of Taylor series in Cⁿ [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy--Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in Cⁿ are constructed and the Taylor series expansion is deduced.

Key words: Polar coordinates, Taylor series, holomorphic functions