article · Journal of Physics A Mathematical and General · 1998
A direct proof of Kim's identities
Cited by 7Open access
Abstract
As a by-product of a finite-size Bethe Ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic theta constants. However, they contain factors like $1 - q^{\sqrt{n}}$ and $1 - q^{n^2}$, instead of $1 - q^n$. We show here that there is a fourth relation that naturally completes the set, in much the same way that there are four relations for the four elliptic theta functions. We derive all of them directly by proving and using a specialization of Weierstrass' factorization theorem in complex variable theory.
Cite this paper
Baxter, R. J. (1998). A direct proof of Kim's identities. Journal of Physics A Mathematical and General, 31(3), 1105–1108. https://doi.org/10.1088/0305-4470/31/3/020
Baxter, R. J. “A direct proof of Kim's identities.” Journal of Physics A Mathematical and General, vol. 31, no. 3, 1998, pp. 1105–08, https://doi.org/10.1088/0305-4470/31/3/020.
Baxter, R. J. 1998. “A direct proof of Kim's identities.” Journal of Physics A Mathematical and General 31 (3): 1105–08. https://doi.org/10.1088/0305-4470/31/3/020.
Baxter, R.J. (1998) ‘A direct proof of Kim's identities’, Journal of Physics A Mathematical and General, 31(3), pp. 1105–1108. Available at: https://doi.org/10.1088/0305-4470/31/3/020.
@article{baxter1998direct,
title = {{A direct proof of Kim's identities}},
author = {Baxter, R. J.},
journal = {Journal of Physics A Mathematical and General},
volume = {31},
number = {3},
pages = {1105--1108},
year = {1998},
doi = {10.1088/0305-4470/31/3/020}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.