INCOMPLETE q-GAMMA FUNCTION AND TRICOMI EXPANSION

In this paper, we introduce a q-analogue of the Tricomi expansion for the incomplete q-gamma function. A general method is described for converting a power series into an expansion in incomplete q-gamma function. Also, we use the q-Tricomi expansion for giving a formal proof of the relation between the incomplete gamma function and the exponential integral. Finally, we formally deduce the q-Tricomi expansion via the q-Taylor expansion.