Cvitkovic M, Smith AS, Pande J (2017)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2017
Publisher: IOP PUBLISHING LTD
Book Volume: 50
Pages Range: 1-24
Journal Issue: 26
URI: http://iopscience.iop.org/article/10.1088/1751-8121/aa7213/pdf
The canonical partition function of a two-dimensional lattice gas in a field of randomly placed traps, like many other problems in physics, evaluates to the Gauss hypergeometric function F-2(1)(a, b; c; z) in the limit when one or more of its parameters become large. This limit is difficult to compute from first principles, and finding the asymptotic expansions of the hypergeometric function is therefore an important task. While some possible cases of the asymptotic expansions of 2F1(a, b; c; z) have been provided in the literature, they are all limited by a narrow domain of validity, either in the complex plane of the variable or in the parameter space. Overcoming this restriction, we provide new asymptotic expansions for the hypergeometric function with two large parameters, which are valid for the entire complex plane of z except for a few specific points. We show that these expansions work well even when we approach the possible singularity of 2F1(a, b; c; z), |z| = 1, where the current expansions typically fail. Using our results we determine asymptotically the partition function of a lattice gas in a field of traps in the different possible physical limits of few/many particles and few/many traps, illustrating the applicability of the derived asymptotic expansions of the HGF in physics.
APA:
Cvitkovic, M., Smith, A.-S., & Pande, J. (2017). Asymptotic expansions of the hypergeometric function with two large parameters-application to the partition function of a lattice gas in a field of traps. Journal of Physics A: Mathematical and Theoretical, 50(26), 1-24. https://dx.doi.org/10.1088/1751-8121/aa7213
MLA:
Cvitkovic, Mislav, Ana-Suncana Smith, and Jayant Pande. "Asymptotic expansions of the hypergeometric function with two large parameters-application to the partition function of a lattice gas in a field of traps." Journal of Physics A: Mathematical and Theoretical 50.26 (2017): 1-24.
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