zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

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