Multivariate padé approximants, fourier series, and applications

Padé逼近是泰勒级数的有理推广，已被研究了一个多世纪。Hermite关于e超越的证明涉及到构造这样的近似式。他的学生帕德系统地研究了这些近似物，并得到了他的名字。多变量Padé逼近的研究相对较新，部分原因是涉及的计算困难，并适合于用计算机代数程序包进行实验。我们的部分意图是使研究尽可能系统化，并构建尽可能多的显式近似。在过去的几年里，我们成功地构造了一些多元函数的显式多元Padé逼近。这一提议的一部分是保持势头，探索更明确的构建。

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.