Preprint Article Version 1 This version is not peer-reviewed

Some Identities for a Sequence of Unnamed Polynomials Connected with the Bell Polynomials

Version 1 : Received: 10 August 2017 / Approved: 11 August 2017 / Online: 11 August 2017 (13:51:05 CEST)

A peer-reviewed article of this Preprint also exists.

Qi, F.; Niu, D.-W.; Guo, B.-N. Some identities for a sequence of unnamed polynomials connected with the Bell polynomials. RACSAM 2018, doi:10.1007/s13398-018-0494-z. Qi, F.; Niu, D.-W.; Guo, B.-N. Some identities for a sequence of unnamed polynomials connected with the Bell polynomials. RACSAM 2018, doi:10.1007/s13398-018-0494-z.

Journal reference: Revista de la Real Academia de Ciencias Exactas, F\'isicas y Naturales--Serie A: Matem\'aticas 2019, 112
DOI: 10.1007/s13398-018-0494-z

Abstract

In the paper, using two inversion theorems for the Stirling numbers and binomial coecients, employing properties of the Bell polynomials of the second kind, and utilizing a higher order derivative formula for the ratio of two di erentiable functions, the authors present two explicit formulas, a determinantal expression, and a recursive relation for a sequence of unnamed polynomials, derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, and recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials.

Subject Areas

identity; Bell polynomial; unnamed polynomial; explicit formula; inversion theorem; Stirling number; binomial coefficient

Readers' Comments and Ratings (4)

Comment 1
Received: 15 August 2017
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first author of this preprint
Comment: In the paper, using two inversion theorems for the Stirling numbers and binomial coefficients, employing properties of the Bell polynomials of the second kind, and utilizing a higher order derivative formula for the ratio of two differentiable functions, the authors present two explicit formulas, a determinantal expression, and a recursive relation for a sequence of unnamed polynomials, derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, and recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials.
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Comment 2
Received: 5 January 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author of this manuscript
Comment: This manuscript has been formally accepted on 4 January 2018 by the Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales--Serie A: Matemáticas
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Comment 3
Received: 15 January 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author
Comment: The DOI code for the formally published version of this preprint is

https://doi.org/10.1007/s13398-018-0494-z
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Comment 4
Received: 21 January 2018
Commenter: Feng Qi
Commenter's Conflict of Interests: I am the first and corresponding author
Comment: https://qifeng618.wordpress.com/2018/01/21/sharing-information-for-some-identities-for-a-sequence-of-unnamed-polynomials-connected-with-the-bell-polynomials/

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