https://doi.org/10.1140/epjs/s11734-025-01511-4
Regular Article
Chisholmd.wl: automated rational approximant for bi-variate series
1
Centre for High Energy Physics, Indian Institute of Science, 560012, Bangalore, Karnataka, India
2
Asia Pacific Center for Theoretical Physics, 77 Cheongam-ro, Nam-gu, Pohang-si, 37673, Gyeongsangbuk-do, Korea
3
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, 606-8502, Kyoto, Japan
a
pathak.tanay@yukawa.kyoto-u.ac.jp
Received:
4
January
2025
Accepted:
5
February
2025
Published online:
5
March
2025
The Chisholm rational approximant is a natural generalization to two variables of the well-known single variable Padé approximant, and has the advantage of reducing to the latter when one of the variables is set equal to 0. 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 also construct suitable approximants around general point (x, y) which 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, 
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 along with various notebooks containing various examples discussed in the paper is available in the https://github.com/TanayPathak-17/Chrisholm_Approximant GitHub repository.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
