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

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URI: https://hdl.handle.net/10016/6610
ISSN: 0377-0427
DOI: 10.1016/S0377-0427(02)00615-5
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2003-04
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Elsevier
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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.
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11 pages, no figures.-- MSC2000 codes: 81V55, 33C45, 81Q10.-- Issue title: "Proceedings of the 6th International Symposium on Orthogonal Polynomials, Special Functions and their Applications" (OPSFA-VI, Rome, Italy, 18-22 June 2001).
MR#: MR1985711 (2004f:33026)
Zbl#: Zbl 1017.81048
Keywords
Varying orthogonal polynomials, Laguerre polynomials, Connection problems, Generalized hypergeometric functions, Morse potential, Pöschl–Teller potential
Bibliographic citation
Journal of Computational and Applied Mathematics, 2003, vol. 153, n. 1-2, p. 411-421
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