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Harmonic Function Theory and Mathematica

Sheldon Axler
Organization: San Francisco State University
Department: Dean of the College of Science and Engineering
Education level


Many of the algorithms used by this software are based on material in the book Harmonic Function Theory by Springer-Verlag in its Graduate Texts in Mathematics series. The software can be used without the book, just as the book can be used without the software.

The HarmonicFunctionTheory Mathematica package performs symbolic manipulation of expressions that arise in the study of harmonic functions. This software, which is available electronically without charge, can perform symbolic calculations that would take a prohibitive amount of time if done without a computer. For example, the Poisson integral of any polynomial can be computed exactly.

Some of the capabilities of our software:

  • symbolic calculus in Rn
  • Dirichlet problem for balls, annular regions, and exteriors of balls in Rn
  • Neumann problem for balls and exteriors of balls in Rn
  • biDirichlet problem for balls in Rn
  • the Bergman projection problem for balls in Rn
  • finding bases for spherical harmonics in Rn
  • explicit formulas for zonal harmonics in Rn
  • manipulations with the Kelvin transform
  • Schwarz functions for balls in Rn
  • harmonic conjugation in R2

*Mathematics > Calculus and Analysis > Harmonic Analysis
Related items

*Harmonic Function Theory and Mathematica   [in MathSource: Packages and Programs]