Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 105, 11 pages      arXiv:1212.6123      https://doi.org/10.3842/SIGMA.2012.105
Contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”

Separation of Variables and Contractions on Two-Dimensional Hyperboloid

Ernie Kalnins a, George S. Pogosyan b, c and Alexander Yakhno c
a) Department of Mathematics, University of Waikato, Hamilton, New Zealand
b) International Center for Advanced Studies, Yerevan State University, A. Manougian 1, Yerevan, 0025, Armenia
c) Departamento de Matemáticas, CUCEI, Universidad de Guadalajara, Jalisco, Mexico

Received August 09, 2012, in final form December 19, 2012; Published online December 26, 2012

Abstract
In this paper analytic contractions have been established in the R→∞ contraction limit for exactly solvable basis functions of the Helmholtz equation on the two-dimensional two-sheeted hyperboloid. As a consequence we present some new asymptotic formulae.

Key words: analytic contraction; separation of variables; Lie group; Helmholtz equation.

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