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1: 24.18 Physical Applications
Bernoulli polynomials appear in statistical physics (Ordóñez and Driebe (1996)), in discussions of Casimir forces (Li et al. (1991)), and in a study of quark-gluon plasma (Meisinger et al. (2002)). Euler polynomials also appear in statistical physics as well as in semi-classical approximations to quantum probability distributions (Ballentine and McRae (1998)).
2: 32.16 Physical Applications
Statistical Physics
Statistical physics, especially classical and quantum spin models, has proved to be a major area for research problems in the modern theory of Painlevé transcendents. …
3: 17.17 Physical Applications
§17.17 Physical Applications
4: Bibliography G
  • C. D. Godsil, M. Grötschel, and D. J. A. Welsh (1995) Combinatorics in Statistical Physics. In Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grötschel, and L. Lovász (Eds.), pp. 1925–1954.
  • 5: Bibliography L
  • E. M. Lifshitz and L. P. Pitaevskiĭ (1980) Statistical Physics, Part 2: Theory of the Condensed State. Pergamon Press, Oxford.
  • 6: Bibliography M
  • A. M. Mathai (1993) A Handbook of Generalized Special Functions for Statistical and Physical Sciences. Oxford Science Publications, The Clarendon Press Oxford University Press, New York.
  • B. M. McCoy (1992) Spin Systems, Statistical Mechanics and Painlevé Functions. In Painlevé Transcendents: Their Asymptotics and Physical Applications, D. Levi and P. Winternitz (Eds.), NATO Adv. Sci. Inst. Ser. B Phys., Vol. 278, pp. 377–391.
  • E. W. Montroll (1964) Lattice Statistics. In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.), University of California Engineering and Physical Sciences Extension Series, pp. 96–143.
  • 7: 26.20 Physical Applications
    §26.20 Physical Applications
    The latter reference also describes chemical applications of other combinatorial techniques. Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993). For an application of statistical mechanics to combinatorics, see Bressoud (1999). …
    8: Bibliography
  • S. V. Aksenov, M. A. Savageau, U. D. Jentschura, J. Becher, G. Soff, and P. J. Mohr (2003) Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics. Comput. Phys. Comm. 150 (1), pp. 1–20.
  • 9: 8.23 Statistical Applications
    §8.23 Statistical Applications
    10: Bibliography B
  • R. Blackmore, U. Weinert, and B. Shizgal (1986) Discrete ordinate solution of a Fokker-Planck equation in laser physics. Transport Theory Statist. Phys. 15 (1-2), pp. 181–210.