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Partial differential approximants and the elucidation of multisingularities

  • Daniel F. Styer
  • Michael E. Fisher
Critical Phenomena
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

Abstract

A partial differential approximant, or PDA, F(x,y), can accurately approximate a two-variable function, f(x,y), on the basis of its power series expansion even near a multisingular point where the function is intrinsically nonanalytic in both variables. This brief review argues that multisingularities occur frequently in two-variable functions arising in practical situations. Partial differential approximants are defined and it is shown why they can approximate multisingularities. The invariance of PDAs under a change of variables is discussed and new results are presented concerning functions exactly representable by PDAs. Finally, several applications of PDAs are mentioned.

Keywords

Ising Model Scaling Function Power Series Expansion Singular Locus Common Zero 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Daniel F. Styer
    • 1
  • Michael E. Fisher
    • 2
  1. 1.Hill Center, Busch CampusRutgers UniversityNew BrunswickUSA
  2. 2.Baker LaboratoryCornell UniversityIthacaUSA

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