Summary: The main object of this paper is to give
-extensions of several explicit relationships of H. M. Srivastava
and A. Pintér
[Appl. Math. Lett. 17, No. 4, 375–380 (2004; Zbl 1070.33012
)] between the Bernoulii and Euler polynomials. We also derive several other formulas in series of Carlitz’s
-Stirling numbers of the second kind.