A new generalization of Apostol type Hermite–Genocchi polynomials and its applications

By using the modified Milne-Thomson’s polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803–2808, 2014), we introduce a new concept of the Apostol Hermite–Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae a...

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Autores principales: Araci, Serkan, Khan, Waseem A., Acikgoz, Mehmet, Özel, Cenap, Kumam, Poom
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4920752/
https://www.ncbi.nlm.nih.gov/pubmed/27386309
http://dx.doi.org/10.1186/s40064-016-2357-4
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author Araci, Serkan
Khan, Waseem A.
Acikgoz, Mehmet
Özel, Cenap
Kumam, Poom
author_facet Araci, Serkan
Khan, Waseem A.
Acikgoz, Mehmet
Özel, Cenap
Kumam, Poom
author_sort Araci, Serkan
collection PubMed
description By using the modified Milne-Thomson’s polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803–2808, 2014), we introduce a new concept of the Apostol Hermite–Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different analytical means and generating functions method. The results obtained here are an extension of Hermite–Bernoulli polynomials (Pathan and Khan in Mediterr J Math 12:679–695, 2015a) and Hermite–Euler polynomials (Pathan and Khan in Mediterr J Math 2015b, doi:10.1007/s00009-015-0551-1) to Apostol type Hermite–Genocchi polynomials defined in this paper.
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spelling pubmed-49207522016-07-06 A new generalization of Apostol type Hermite–Genocchi polynomials and its applications Araci, Serkan Khan, Waseem A. Acikgoz, Mehmet Özel, Cenap Kumam, Poom Springerplus Research By using the modified Milne-Thomson’s polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803–2808, 2014), we introduce a new concept of the Apostol Hermite–Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different analytical means and generating functions method. The results obtained here are an extension of Hermite–Bernoulli polynomials (Pathan and Khan in Mediterr J Math 12:679–695, 2015a) and Hermite–Euler polynomials (Pathan and Khan in Mediterr J Math 2015b, doi:10.1007/s00009-015-0551-1) to Apostol type Hermite–Genocchi polynomials defined in this paper. Springer International Publishing 2016-06-24 /pmc/articles/PMC4920752/ /pubmed/27386309 http://dx.doi.org/10.1186/s40064-016-2357-4 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
Araci, Serkan
Khan, Waseem A.
Acikgoz, Mehmet
Özel, Cenap
Kumam, Poom
A new generalization of Apostol type Hermite–Genocchi polynomials and its applications
title A new generalization of Apostol type Hermite–Genocchi polynomials and its applications
title_full A new generalization of Apostol type Hermite–Genocchi polynomials and its applications
title_fullStr A new generalization of Apostol type Hermite–Genocchi polynomials and its applications
title_full_unstemmed A new generalization of Apostol type Hermite–Genocchi polynomials and its applications
title_short A new generalization of Apostol type Hermite–Genocchi polynomials and its applications
title_sort new generalization of apostol type hermite–genocchi polynomials and its applications
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4920752/
https://www.ncbi.nlm.nih.gov/pubmed/27386309
http://dx.doi.org/10.1186/s40064-016-2357-4
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