SOME PROPERTIES AND AN APPLICATION OF MULTIVARIATE EXPONENTIAL POLYNOMIALS
Résumé
In the paper, the authors introduce a notion " multivariate exponential polynomials " which generalize exponential numbers and polynomials, establish explicit formulas, inversion formulas, and recurrence relations for multivariate exponential polynomials in terms of the Stirling numbers of the first and second kinds with the help of theFà a di Bruno formula, two identities for the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds, construct some determinantal inequalities and product inequalities for multivariate exponential polynomials with the aid of some properties of completely monotonic functions and other known results, derive the logarithmic convexity and logarithmic concavity for multivariate exponential polynomials, and finally find an application of multi-variate exponential polynomials to white noise distribution theory by confirming that multivariate exponential polynomials satisfy conditions for sequences required in white noise distribution theory.
Mots clés
Bell number
Touchard polynomial
multi-order exponential number
property
multivariate exponential polynomial
inversion theorem
Bell polynomial of the second kind
Stirling number
completely monotonic function
recurrence relation
white noise distribution theory
product inequality
logarithmic concavity
logarithmic convexity
Faa di Bruno formula
exponential polynomial
explicit formula
inversion formula
determinantal inequality
Origine : Fichiers produits par l'(les) auteur(s)
Loading...