References
- Abel, N. (1828). Recherches sur les fonctions elliptiques. J. Reine Angew. Math. 3: 160–190. DOI: 10.1515/crll.1828.3.160.
- Beenakker, C. (2020). An identity between two elliptic integrals. Mathoverflow. Accessed on Jan 4, 2020. Available at: mathoverflow.net/questions/349272
- Borwein, J. M., Glasser, M. L., McPhedran, R. C., Wan, J. G., Zucker, I. J. (2013). Lattice Sums Then and Now. Cambridge: Cambridge Univ. Press.
- Bowman, F. (1960). An Introduction to Elliptic Functions. New York: Dover.
- Cayley, A. (1895). An Elementary Treatise on Elliptic Functions. London: G. Bell and Sons.
- Chenciner, A., Montgomery, R. (2000). A remarkable periodic solution of the three-body problem in the case of equal masses. Ann. Math. 152(3): 881–901. DOI: 10.2307/2661357.
- Chowla, S., Selberg, A. (1949). On Epstein’s zeta function (I). Proc. Natl. Acad. Sci. 35(7): 371–374. 10.1073/pnas.35.7.371
- Cox, D. A. (2013). Primes of the Form x2+ny2, 2nd ed. New York: Wiley.
- Fujiwara, T., Fukada, H., Ozaki, H. (2003). Choreographic three bodies on the lemniscate. J. Phys. A Math. Gen. 36(11): 2791–2800. DOI: 10.1088/0305-4470/36/11/310.
- Heath, T. L. (1956). Euclid: The Thirteen Books of the Elements. New York: Dover.
- Joyce, G. S., Delves, R. T., Zucker, I. J. (2003). Exact evaluation for the anisotropic face-centered and simple cubic lattices. J. Phys. A Math. Gen. 36(32): 8661–8672. DOI: 10.1088/0305-4470/36/32/307.
- Legendre, A.-M. (1811). Exercices de Calcul Intégral sur Divers Ordres de Transcendantes et sur les Quadratures. Paris: Courcier.
- Liouville, J. (1833). Mémoire sur la détermination des intégrales dont la valeur est algébrique. J. École Polytechnique 14: 124–193.
- Moore, C. (1993). Braids in classical dynamics. Phys. Rev. Lett. 70(24): 3675–3679. 10.1103/PhysRevLett.70.3675
- Ramanujan, S. (1914). Modular equations and approximations to π. Q J. Math. XLV: 350–372.
- Reid, C. (1996). Hilbert. New York: Springer.
- Schwarz, H. A. (1869). Ueber einige Abbildungsaufgaben. J. Reine Angew. Math. 70: 105–120. DOI: 10.1515/crll.1869.70.105.
- Simó, C. (2001). Periodic orbits of planar N-body problem with equal masses and all bodies on the same path. In: Steves, B. A., Maciejewski, A. J., eds. The Restless Universe. London: Institute of Physics Publishing, pp. 265–283.
- Wikipedia. (2014). Three-body problem. Accessed on Sept 19, 2020. Available at: en.wikipedia.org/wiki/Three-body_problem
- Watson, G. N. (1939). Three triple integrals. Q. J. Math. 10(1): 266–276. DOI: 10.1093/qmath/os-10.1.266.
- Whittaker, E. T., Watson, G. N. (1960). A Course of Modern Analysis. Cambridge: Cambridge Univ. Press.