Multivariate padé approximants, fourier series, and applications

Padé逼近是Taylor级数的一种有理推广，已经被研究了世纪。厄米的超越性的证明e涉及建设这样的逼近。他的学生Padé探讨了逼近系统，并得到了他的名字附加到他们。多元Padé逼近的研究是相对较新的，部分原因是涉及的计算困难，并适合于计算机代数软件包的实验。我们的部分意图是使尽可能多的研究尽可能系统，并构造尽可能多的显式逼近。在过去的几年中，我们成功地构造了一些多元函数的显式多元Padé逼近。这个建议的一部分是保持势头，探索更明确的结构。

Padé approximants are a rational generalization of Taylor series and have been studied for over a century. Hermite's proof of transcendence of e involved constructing such approximants. His student Padé explored the approximants systematically and got his name attached to them. The study of multivariate Padé approximants is relatively new, partly because of the computation difficulties involved, and lends itself to experimentation with computer algebra packages. Part of our intention is to make as much of the study as systematic as possible, and to construct as many of the explicit approximants as we can. In the past few years, we successfully constructed explicit multivariate Padé approximants to some multivariate functions. Part of this proposal is to keep the momentum and explore more explicit constructions.