Some Formulas Related to Residue Method

Su-Dan Wang1, Wuyungaowa 1
1 Department of Mathematics, College of Sciences and Technology, Inner Mongolia University, Hohhot 010021, P. R. China

Abstract

In this paper, with the help of the residue method, we find some interesting formulas relating residue and ordinary Bell polynomials, \(\hat{B}_{n,k}(x_1,x_2,\ldots)\). Further, we prove identities involving some combinatorial numbers to demonstrate the application of the formulas.

Keywords: residue; formal power series; forma] Laurent series; gen- erating function; ordinary Bell polynomials Classification AMS(2000): 05A10, 05A19