Rational approximants defined from double power series

Chisholm, J. S. R.

doi:10.1090/S0025-5718-1973-0382928-6

Rational approximants defined from double power series
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by J. S. R. Chisholm PDF

Math. Comp. 27 (1973), 841-848 Request permission

Abstract:

Rational approximants are defined from double power series in variables x and y, and it is shown that these approximants have the following properties: (i) they possess symmetry between x and y; (ii) they are in general unique; (iii) if $x = 0$ or $y = 0$, they reduce to diagonal Padé approximants; (iv) their definition is invariant under the group of transformations $x = Au/(1 - Bu),y = Av/(1 - Cv)$ with $A \ne 0$; (v) an approximant formed from the reciprocal series is the reciprocal of the corresponding original approximant. Possible variations, extensions and generalisations of these results are discussed.

References

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