Expansions in series of varying Laguerre polynomials and some applications to molecular potentials

Authors:
J. Sánchez-Ruiz;P. López-Artés;J. S. Dehesa
Affiliations:
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid, Spain and Instituto Carlos I de Física Teórica y Computacional ...;Departamento de Estadística y Matemática Aplicada, Universidad de Almería, 04120 Almería, Spain;Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain and Departamento de Física Moderna, Universidad de Granada, 18071 Granada, Spain
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Year:
2003

Citing 6
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Abstract

The expansion of a large class of functions in series of linearly varying Laguerre polynomials, i.e., Laguerre polynomials whose parameters are linear functions of the degree, is found by means of the hypergeometric functions approach. This expansion formula is then used to obtain the Brown-Carlitz generating function (which gives a characterization of the exponential function) and the connection formula for these polynomials. Finally, these results are employed to connect the bound states of the quantum-mechanical potentials of Morse and Pöschl-Teller, which are frequently used to describe molecular systems.