Submitted:
22 September 2017
Posted:
23 September 2017
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Abstract
In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.
Keywords:
multivariate logarithmic polynomial
; generating function
; completely monotonic function
; Bernstein function
; integral representation
; Lévy-Khintchine representation
; real part
; imaginary part
; uniform convergence
; recurrence relation
; mathematical induction
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