Short-range oscillators in a power-series picture

The class of short-range potentials V-[M](X) = (m=2)Sigma(M) (f(m) + g(m) s inh x)/cosh(m) x is considered as an asymptotically vanishing phenomenologi cal alternative to the popular anharmonic long-range V(x) = (n=2)Sigma(N) h (n)x(n) We propose a method which parallels the analytic Hill-Taylor descri ption of anharmonic oscillators and represents all the wavefunctions psi([M ])(x) non-numerically, in terms of certain infinite hypergeometric-like ser ies. In this way the well known exact M = 2 solution is generalized to any M > 2.