Integral representations of analytic and harmonic functions

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.