Integral Representations of Analytic and Harmonic Functions

被引：0

作者：

Bavrin, I. I. ^{[1
]}

机构：

[1] Moscow State Pedag Univ, Moscow 119882, Russia

来源：

DOKLADY MATHEMATICS | 2011年 / 83卷 / 03期

关键词：

Harmonic Function; Integral Representation; Complex Variable; Arbitrary Point; Gamma Function;

D O I：

10.1134/S106456241103032X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

New integral representations are established for analytic and harmonic functions in the disk. A function that is holomorphic in the disk and a harmonic function in the same disk is considered. An arbitrary point and a circle centered at the origin with a certain radius are also considered. For a harmonic function in the disk, the values of f (z) at the other points of this disk are found. The obtained results are found to be similar to Cauchy, Schwarz, and Poisson integral formulas.

引用

页码：364 / 366

页数：3

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