Preprint Article Version 1 This version is not peer-reviewed

Integral Representations for Multivariate Logarithmic Polynomials

Version 1 : Received: 22 September 2017 / Approved: 23 September 2017 / Online: 23 September 2017 (10:55:57 CEST)

A peer-reviewed article of this Preprint also exists.

Qi, F. Integral Representations for Multivariate Logarithmic Polynomials. Journal of Computational and Applied Mathematics 2018, in press. Qi, F. Integral Representations for Multivariate Logarithmic Polynomials. Journal of Computational and Applied Mathematics 2018, in press.

Journal reference: Journal of Computational and Applied Mathematics 2018
DOI: https://doi.org/10.1016/j.cam.2017.11.047

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.

Subject Areas

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

Readers' Comments and Ratings (6)

Comment 1
Received: 24 December 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the author of this preprint.
Comment: This manuscript has been accepted on 25 December 2017 for publication in the Journal of Computational and Applied Mathematics.
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Comment 2
Received: 4 January 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the author
Comment: This preprint has been formally published as

Feng Qi, Integral representations for multivariate logarithmic polynomials, Journal of Computational and Applied Mathematics (2018), in press; Available online at https://doi.org/10.1016/j.cam.2017.11.047
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Comment 3
Received: 17 January 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the author
Comment: Elsevier
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Comment 4
Received: 17 January 2018
Commenter: Feng Qi (Click to see Publons profile: )
Commenter's Conflict of Interests: I am the author
Comment: Please cite this article as

Feng Qi, Integral representations for multivariate logarithmic polynomials, Journal of Computational and Applied Mathematics 336 (2018), 5462; Available online at https://doi.org/10.1016/j.cam.2017.11.047

F. Qi, Integral representations for multivariate logarithmic polynomials, J. Comput. Appl. Math. 336 (2018), 54
62; Available online at https://doi.org/10.1016/j.cam.2017.11.047
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Response 1 to Comment 4
Received: 17 January 2018
Commenter: Feng Qi (Click to see Publons profile: )
The commenter has declared there is no conflict of interests.
Comment: Feng Qi, Integral representations for multivariate logarithmic polynomials, Journal of Computational and Applied Mathematics 336 (2018), 5462; Available online at https://doi.org/10.1016/j.cam.2017.11.047

F. Qi, Integral representations for multivariate logarithmic polynomials, J. Comput. Appl. Math. 336 (2018), 54
62; Available online at https://doi.org/10.1016/j.cam.2017.11.047
Comment 5
Received: 20 April 2018
Commenter: Feng Qi (Click to see Publons profile: )
The commenter has declared there is no conflict of interests.
Comment: Feng Qi, Integral representations for multivariate logarithmic polynomials, Journal of Computational and Applied Mathematics 336 (2018), 54--62; Available online at https://doi.org/10.1016/j.cam.2017.11.047
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