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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Analysis and applications of holomorphic functions in higher dimensions


Author: R. Z. Yeh
Journal: Trans. Amer. Math. Soc. 345 (1994), 151-177
MSC: Primary 26E05; Secondary 30G35, 31B05, 35C10, 35J99
Erratum: Trans. Amer. Math. Soc. 347 (1995), null.
MathSciNet review: 1260207
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1260207-2
PII: S 0002-9947(1994)1260207-2
Keywords: Hypercomplex numbers, holomorphic functions, Cauchy-Riemann equations, symmetric powers, Stieltjes line integrals, Taylor formula, Cauchy integral formula, divergence theorem, Leibniz's rule, power series, harmonic functions, Poisson equation, Laplace equation, polynomial expansions
Article copyright: © Copyright 1994 American Mathematical Society