Partial differential approximants and the elucidation of multisingularities
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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.
KeywordsIsing Model Scaling Function Power Series Expansion Singular Locus Common Zero
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