Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials

In 2008, Liu and Wang established various symmetric identities for Bernoulli, Euler and Genocchi polynomials. In this paper, we extend these identities in a unified and generalized form to families of Hermite–Bernoulli, Euler and Genocchi polynomials. The procedure followed is that of generating fun...

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Detalles Bibliográficos
Autores principales: Khan, Waseem A., Haroon, Hiba
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5097062/
https://www.ncbi.nlm.nih.gov/pubmed/27872796
http://dx.doi.org/10.1186/s40064-016-3585-3
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author Khan, Waseem A.
Haroon, Hiba
author_facet Khan, Waseem A.
Haroon, Hiba
author_sort Khan, Waseem A.
collection PubMed
description In 2008, Liu and Wang established various symmetric identities for Bernoulli, Euler and Genocchi polynomials. In this paper, we extend these identities in a unified and generalized form to families of Hermite–Bernoulli, Euler and Genocchi polynomials. The procedure followed is that of generating functions. Some relevant connections of the general theory developed here with the results obtained earlier by Pathan and Khan are also pointed out.
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spelling pubmed-50970622016-11-21 Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials Khan, Waseem A. Haroon, Hiba Springerplus Research In 2008, Liu and Wang established various symmetric identities for Bernoulli, Euler and Genocchi polynomials. In this paper, we extend these identities in a unified and generalized form to families of Hermite–Bernoulli, Euler and Genocchi polynomials. The procedure followed is that of generating functions. Some relevant connections of the general theory developed here with the results obtained earlier by Pathan and Khan are also pointed out. Springer International Publishing 2016-11-04 /pmc/articles/PMC5097062/ /pubmed/27872796 http://dx.doi.org/10.1186/s40064-016-3585-3 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Khan, Waseem A.
Haroon, Hiba
Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials
title Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials
title_full Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials
title_fullStr Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials
title_full_unstemmed Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials
title_short Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials
title_sort some symmetric identities for the generalized bernoulli, euler and genocchi polynomials associated with hermite polynomials
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5097062/
https://www.ncbi.nlm.nih.gov/pubmed/27872796
http://dx.doi.org/10.1186/s40064-016-3585-3
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