Analysis and applications of holomorphic functions in higher dimensions

Yeh, R. Z.

doi:10.1090/S0002-9947-1994-1260207-2

Analysis and applications of holomorphic functions in higher dimensions
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Trans. Amer. Math. Soc. 345 (1994), 151-177 Request permission

Erratum: Trans. Amer. Math. Soc. 347 (1995), 1081.

Abstract:

Holomorphic functions in ${R^n}$ are defined to generalize those in ${R^2}$. A Taylor formula and a Cauchy integral formula are presented. An application of the Taylor formula to the kernel of the Cauchy integral formula results in Taylor series expansions of holomorphic functions. Real harmonic functions are expanded in series of homogeneous harmonic polynomials.

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