Volume 9, 2003, Number 4

Generalizations of the polynomials of Bernoulli, Euler and Hermite are defined here in terms of generalized integers called Fermatian integers. These are closely related to the q-series extensively studied by Leonard Carlitz. These various analogues of the classical special functions are inter-related with one another and also to some of the problems posed by Morgan Ward. The works of Henry Gould and Vern Hoggatt are also extensively cited.

By using q-Volkenborn integration, the multiple Changhee q-Bernoulli numbers which are an interesting analogue of Barnes’ multiple Bernoulli numbers were constructed in [4]. The object of this paper is to define the extension of multiple Changhee q-Bernoulli numbers and to give the new explicit formulas which are related to these numbers.