It is shown that the polynomials introduced recently by Aldaya, Bisquert, and Navarro-Salas [Phys. Lett. A 156, 381 (1991)] in connection with a relativistic generalization of the quantum harmonic oscillator can be expressed in terms of Gegenbauer polynomials. This fact is useful in the investigation of the properties of the corresponding wave function. Some examples are given, in particular, related to the asymptotic behavior and to the distribution of zeros of the polynomials for large quantum numbers.

This is a reproduction, with minor corrections and an added Appendix, of a paper published in J. Bertrand et al.(Eds.), Modern Group Theoretical Methods in Physics, Kluwer Academic Publishers 1995.1 We follow the convention used e.g. in the first and third references in [1]; sometimes the squeezing operator is defined with the opposite signs in the exponent.

An expansion of the hypergeometric function F12(a,b,c+1;−z2/4ab) in Bessel functions of argument z is derived. This expansion can be used to obtain an asymptotic expansion of the hypergeometric function for large absolute values of a and b.

The edge of the wedge theorem is generalized to the case where one only assumes the existence and equality of the distribution boundary values of /_j_ (z) and all their derivatives on some analytic curve Ή in R n . Here / ± (z) are holomorphic in E n i iC, respectively, where C is a convex cone, and ^ has its tangent vector in C at every point. Under these assumptions there exists an analytic continuation f(z) holomorphic in some complex neighbourhood of the double cone generated by #. A proof is also given of the connection between the existence of a distribution boundary value and the growth of the holomorphic function near the boundary.

No abstract