In this chapter, we construct rational approximations of PSWFs. More specifically, we approximate the reciprocal of ψn in the interval ( −1,1) by a rational function having n poles (these poles happen to be precisely the n roots of ψn in (−1,1)). Also, we derive explicit bounds on the error of such approximations. The underlying analysis is based on a detailed investigation of certain properties of PSWFs outside the interval (−1,1) (see also [49, 50]).
Rational Approximation Prolate Index Boundary Term Fourth Column Principal Result
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A. Osipov, V. Rokhlin, Detailed analysis of prolate quadratures and interpolation formulas, Yale CS Technical Report #1458, 2012.Google Scholar
A. Osipov, V. Rokhlin, Detailed analysis of prolate quadratures and interpolation formulas, arXiv:1208.4816v1, 2012.Google Scholar