Difference equations revisited. (English) Zbl 0639.39002
Mathematical quantum field theory and related topics, Proc. Conf., Montreal/Can. 1987, CMS Conf. Proc. 9, 73-82 (1988).
[For the entire collection see Zbl 0632.00022.]
The author reviews some basic connections between difference equations, continued fractions, Jacobi matrices and orthogonal polynomials, with emphasis on the large n boundary-value solutions to the difference equation. A basic hypergeometric general solution to the q-difference equation associated with Ramanujan type continued fraction and Al-Salam- Chibea polynomials is presented as a generalization of the hypergeometric solution associated with the Meixner-Pollaczek polynomials. Applications to Schrödinger type operators are mentioned.
The author reviews some basic connections between difference equations, continued fractions, Jacobi matrices and orthogonal polynomials, with emphasis on the large n boundary-value solutions to the difference equation. A basic hypergeometric general solution to the q-difference equation associated with Ramanujan type continued fraction and Al-Salam- Chibea polynomials is presented as a generalization of the hypergeometric solution associated with the Meixner-Pollaczek polynomials. Applications to Schrödinger type operators are mentioned.
Reviewer: R.Vaillancourt
MSC:
| 39A10 | Additive difference equations |
| 40A15 | Convergence and divergence of continued fractions |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
| 44A60 | Moment problems |
| 47A10 | Spectrum, resolvent |
| 47A40 | Scattering theory of linear operators |
