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Journal Articles Mathematical Methods in the Applied Sciences Year : 2020

SOME PROPERTIES AND AN APPLICATION OF MULTIVARIATE EXPONENTIAL POLYNOMIALS

Abstract

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 the Fàa 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.
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Dates and versions

hal-01745173 , version 1 (28-03-2018)
hal-01745173 , version 2 (06-03-2020)

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Feng Qi, Da-Wei Niu, Dongkyu Lim, Bai-Ni Guo. SOME PROPERTIES AND AN APPLICATION OF MULTIVARIATE EXPONENTIAL POLYNOMIALS. Mathematical Methods in the Applied Sciences, 2020, 43 (6), pp.2967--2983. ⟨10.1002/mma.6095⟩. ⟨hal-01745173v2⟩
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