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.
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Styer, D.F., Fisher, M.E. (1984). Partial differential approximants and the elucidation of multisingularities. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072421
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DOI: https://doi.org/10.1007/BFb0072421
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