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.
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.
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.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
Received:
17 January 2018
Commenter:
Feng Qi
Commenter's Conflict of Interests:
I am the author
Comment:
Elsevier
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Dear Professor Qi,
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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), 5462; Available online at https://doi.org/10.1016/j.cam.2017.11.047
(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), 5462; Available online at https://doi.org/10.1016/j.cam.2017.11.047
(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
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the author of this preprint.
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the author
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
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the author
Share your article!
cover
Dear Professor Qi,
We are pleased to let you know that the final version of your article Integral representations for multivariate logarithmic polynomials is now available online, containing full bibliographic details.
To help you access and share this work, we have created a Share Link – a personalized URL providing 50 days' free access to your article. Anyone clicking on this link before March 08, 2018 will be taken directly to the final version of your article on ScienceDirect. No sign up, registration or fees are required – they can simply click and read.
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https://authors.elsevier.com/a/1WPGz1LkiPEkvX
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You can find out more about Share Links on Elsevier.com.
Did you know, as an author, you can use your article for a wide range of scholarly, non-commercial purposes, and share and post your article online in a variety of ways? For more information visit www.elsevier.com/sharing-articles.
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Commenter:
Commenter's Conflict of Interests: I am the author
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), 5462; Available online at https://doi.org/10.1016/j.cam.2017.11.047
Commenter:
The commenter has declared there is no conflict of interests.
F. Qi, Integral representations for multivariate logarithmic polynomials, J. Comput. Appl. Math. 336 (2018), 5462; Available online at https://doi.org/10.1016/j.cam.2017.11.047
Commenter:
The commenter has declared there is no conflict of interests.