Laguerre-based Hermite-Bernoulli polynomials associated with bilateral series

Waseem Ahmad Khan$^1$, Serkan Araci$^2$, Mehmet Acikgoz$^{3}$ and Ayhan Esi$^4$

In the paper, we define Laguerre-based Hermite-Bernoulli polynomial with its generating function, and investigate certain properties. From this generating function, we derive summation formulas and related bilateral series associated with the newly introduced generating function. Some of whose special cases are also presented. Relevant connections of some results presented here with those involving simpler known partly unilateral and partly bilateral representations are also obtained.

Tbilisi Mathematical Journal, Vol. 11(2) (2018), pp. 111121