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A new class of generalized Laguerre–Euler polynomials

  • Nabiullah Khan
  • Talha Usman
  • Junesang Choi
Original Paper
  • 52 Downloads

Abstract

A variety of polynomials, their extensions and variants have been extensively investigated, due mainly to their potential of applications in diverse research areas. In this sequel, we introduce a new class of generalized Laguerre–Euler polynomials and present certain potentially useful formulas and identities such as implicit summation formulae and symmetry identities. The new class of polynomials introduced and the results presented here, being very general, are shown to be specialized to reduce to various known polynomials and to yield some known and new formulas and identities, respectively.

Keywords

Laguerre polynomials Hermite polynomials Bernoulli and generalized Bernoulli polynomials Euler and generalized Euler polynomials Laguerre–Euler polynomials Summation formulae Symmetry identities 

Mathematics Subject Classification

11B68 33C45 33E20 

Notes

Acknowledgements

The authors would like to express their deep-felt thanks for the reviewers’ very helpful and informative comments to improve this paper as it stands.

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Engineering and TechnologyAligarh Muslim UniversityAligarhIndia
  2. 2.Department of MathematicsDongguk UniversityGyeongjuRepublic of Korea

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