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Laguerre-type special functions and population dynamics. (English) Zbl 1117.33001

Recently, in a series of papers, P. E. Ricci and his collaborators investigated some Laguerre-type special functions obtained by the use of the Laguerre derivative operators (containing n+1 derivatives):

D nL :=Dx...DxDxD·

In this paper, the authors introduce new Laguerre type population dynamics models by substituting in classical models the ordinary derivatives with the Laguerre derivatives. The eigenfunctions of D nL are useful in order to approximate different behavior of population growth. The corresponding Laguerre-type of modified logistic, Bernoulli, Gompertz, Allee and Beverton-Holt models were considered. It was shown for these cases that the oscillating asymptotic behavior of solutions takes the place of the ordinary monotonic one.

33B10Exponential and trigonometric functions
33C45Orthogonal polynomials and functions of hypergeometric type