The Chisholm rational approximant is a natural generalization to two variables of the well-known single variable Pad\'e approximant, and has the advantage of reducing to the latter when one of the variables is set equals to 0. We present, to our knowledge, the first automated Mathematica package to evaluate diagonal Chisholm approximants of two variable series. For the moment, the package can only be used to evaluate diagonal approximants i.e. the maximum powers of both the variables, in both the numerator and the denominator, is equal to some integer $M$. We further modify the original method so as to allow us to evaluate the approximants around some general point $(x,y)$ not necessarily $(0,0)$. Using the approximants around general point $(x,y)$, allows us to get a better estimate of the result when the point of evaluation is far from $(0,0)$. Several examples of the elementary functions have been studied which shows that the approximants can be useful for analytic continuation and convergence acceleration purposes. We continue our study using various examples of two variable hypergeometric series, $\mathrm{Li}_{2,2}(x,y)$ etc that arise in particle physics and in the study of critical phenomena in condensed matter physics. The demonstration of the package is discussed in detail and the Mathematica package is provided as an ancillary file.

翻译：Chisholm有理逼近是著名的单变量Padé逼近在双变量情形下的自然推广，其优势在于当其中一个变量设为0时退化为后者。据我们所知，本文提出了首个用于计算双变量级数对角Chisholm逼近的自动化Mathematica程序包。目前该程序包仅能计算对角逼近，即分子与分母中两个变量的最高幂次均等于某个整数$M$。我们进一步改进原始方法，使其能够计算关于一般点$(x,y)$（而非仅限于$(0,0)$）的逼近。利用一般点$(x,y)$周围的逼近，可以在评估点远离$(0,0)$时获得更优的结果估计。通过对多个初等函数实例的研究表明，该逼近可用于解析延拓与收敛加速。我们继续研究粒子物理及凝聚态物理临界现象中出现的双变量超几何级数、$\mathrm{Li}_{2,2}(x,y)$等实例。详细讨论了程序包的演示过程，并随附Mathematica程序包文件。