Comptes Rendus
Number theory/Mathematical analysis
A new generalization of Apostol-type Laguerre–Genocchi polynomials
[Une nouvelle généralisation des polynômes de Laguerre–Genocchi de type Apostol]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 607-617.

Many extensions and variants of the so-called Apostol-type polynomials have recently been investigated. Motivated mainly by those works and their usefulness, we aim to introduce a new class of Apostol-type Laguerre–Genocchi polynomials associated with the modified Milne–Thomson's polynomials introduced by Derre and Simsek and investigate its properties, including, for example, various implicit formulas and symmetric identities in a systematic manner. The new family of polynomials introduced here, being very general, contains, as its special cases, many known polynomials. So the properties and identities presented here reduce to yield those results of the corresponding known polynomials.

Plusieurs extensions et variantes des polynômes dits de type Apostol ont été récemment étudiées. Motivés par ces travaux et leur utilité, notre but est d'introduire une nouvelle classe de polynômes de type Apostol généralisant les polynômes de Laguerre–Genochi associés aux polynômes de Milne–Thompson modifiés, introduits par Derre et Simsek, et d'en étudier de façon systématique les propriétés. Par exemple, nous donnons diverses formules implicites et des identités de symétrie. La nouvelle famille de polynômes introduite ici est très générale et contient comme cas particuliers beaucoup de polynômes connus. Les résultats présentés ici redonnent des propriétés et identités de ces polynômes connus.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.04.010

Nabiullah Khan 1 ; Talha Usman 1 ; Junesang Choi 2

1 Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh, 202002, India
2 Department of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea
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Nabiullah Khan; Talha Usman; Junesang Choi. A new generalization of Apostol-type Laguerre–Genocchi polynomials. Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 607-617. doi : 10.1016/j.crma.2017.04.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.04.010/

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