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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 26E05, 30G35, 31B05, 35C10, 35J99

Retrieve articles in all journals with MSC: 26E05, 30G35, 31B05, 35C10, 35J99

Additional Information

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