Abstract
We apply method of separation of the variables to q-analogs of several equations of mathematical physics.
Similar content being viewed by others
References
Akhiezer, A.I., Berestetskii, V.B.: Quantum Electrodinamics. Interscience Publishers, New York (1965)
Akhiezer, N.I.: Theory of Approximation. Frederick Ungar Publishing Co., New York (1956)
Askey, R.A., Wilson, J.A.: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Memoirs Amer. Math. Soc. 319 (1985)
Atakishiyev, N.M., Suslov, S.K.: Difference hypergeometric functions. In: Gonchar, A.A., Saff, E.B. (eds.) Progress in Approximation Theory: An International Perspective vol. 19, pp. 1–35. Springer Series in Computational Mathematics. Springer–Verlag (1992)
Berestezkii, V.B., Lifshitz, E.M., Pitaevskii, L.P.: Quantum Electrodinamics, 2nd edn. Butterworth–Heinemann, Oxford (1999)
Bary, N.K.: A Treatise on Trigonometric Series, Two volumes. Macmillan, New York (1964)
Davydov, A.S.: Quanmum Mechanics. Pergamon Press, Oxford (1965)
Bustoz, J., Suslov, S.K.: Basic analog of Fourier series on a q-quadratic grid. Methods Appl. Anal. 5, 1–38 (1998)
Gasper, G., Rahman, M.: Basic Hypergeometric Series, 2nd edn. Cambridge University Press, Cambridge (2004)
Jackson, J.D.: Classical Electrodynamics, 2nd edn. John Wiley & Sons, New York (1975)
Landau, L.D., Lifshitz, E.M.: Classical field theory. Fourth Revised English Edition. Butterworth-Heinemann, Oxford (1998)
Nikiforov, A.F., Suslov, S.K., Uvarov, V.B.: Classical Orthogonal Polynomials of a Discrete Variable. Nauka, Moscow, 1985 [in Russian]; English Translation, Springer-Verlag, Berlin (1991)
Ruijsenaars, S.N.M.: First order analytic difference equations and integrable quantum systems. J. Math. Phys. 38, 1069–1146 (1997)
Ruijsenaars, S.N.M.: Special functions associated with Calogero–Moser type quantum systems. In: Harnad, J., Sabidussi, G., Winternitz P. (eds.) Proceedings of the 1999 Montréal Séminaire de Mathématiques Supérieures, CRM Proceedings & Lecture Notes, pp. 1–38. Amer. Math. Soc. (2000)
Ruijsenaars, S.N.M.: On Barnes’ multiple zeta and gamma functions. Advances in Math. 156, 107–132 (2000)
Ruijsenaars, S.N.M.: Special functions defined by analytic difference equations. In: Bustoz, J., Ismail, M.E.H., Suslov, S.K. (eds.) Special Functions 2000: Current Perspective and Future Directions, NATO Science Series II: Mathematics, Physics and Chemistry, vol. 30, pp. 281–333. Kluwer Academic Publishers, Dordrecht-Boston-London (2001)
Suslov, S.K.: “Addition” theorems for some q-exponential and q-trigonometric functions. Methods Appl. Anal. 4, 11–32 (1997)
Suslov, S.K.: Another addition theorem for the q-exponential function. J. Phys. A: Math. Gen. 33, L375–L380 (2000)
Suslov, S.K.: Basic exponential functions on a q-quadratic grid. In: Bustoz, J., Ismail, M.E.H., Suslov, S.K. (eds.) Special Functions 2000: Current Perspective and Future Directions, NATO Science Series II: Mathematics, Physics and Chemistry, vol. 30, pp. 411–456. Kluwer Academic Publishers, Dordrecht-Boston-London (2001)
Suslov, S.K.: Some expansions in basic Fourier series and related topics. J. Approx, Theory 115(2), 289–353 (2002)
Suslov, S.K.: An Introduction to Basic Fourier Series. Kluwer Series Developments in Mathematics, vol. 9. Kluwer Academic Publishers, Dordrecht-Boston-London (2003)
Tolstov, G.P.: Fourier Series. Dover, New York (1962)
Zygmund, A.: Trigonometric Series, 2nd edn. Cambridge University Press, Cambridge (1968)
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Dick Askey on his 70th birthday.
2000 Mathematics Subject Classification Primary—33D45, 42C10; Secondary—33D15.
Rights and permissions
About this article
Cite this article
Ey, K., Ruffing, A. & Suslov, S. Method of separation of the variables for basic analogs of equations of mathematical physics. Ramanujan J 13, 407–447 (2007). https://doi.org/10.1007/s11139-006-0260-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11139-006-0260-2