A new class of generalized Laguerre–Euler polynomials
- 52 Downloads
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.
KeywordsLaguerre polynomials Hermite polynomials Bernoulli and generalized Bernoulli polynomials Euler and generalized Euler polynomials Laguerre–Euler polynomials Summation formulae Symmetry identities
Mathematics Subject Classification11B68 33C45 33E20
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.
- 2.Andrews, L.C.: Special Functions for Engineer and Mathematician. Macmillan Company, New York (1985)Google Scholar
- 11.Khan, N.U., Usman, T., Choi, J.:A new generalization of Apostol type Laguerre–Genocchi polynomials. C. R. Acad. Sci. Paris, Ser. I (2017), http://dx.doi.org/10.1016/j.crma.2017.04.010
- 16.Norlund, N.E.: Vorlesungen uber Differenzenrechun, Springer-Verlag, Berlin 1924. Reprinted by Chelsia Publishing Company, Bronx (1954)Google Scholar
- 19.Rainville, E.D.: Special Functions, Macmillan Company, New York, 1960. Reprinted by Chelsea Publishing Company, Bronx (1971)Google Scholar
- 23.Srivastava, H.M., Manocha, H.L.: A Treatise on Generating Functions, Halsted Press. Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto (1984)Google Scholar