Two interesting infinite product formulas were presented by Choi, Lee and Srivastava [A generalization of Wilf's formula. Kodai Math J. 2003;26:44–48], who generalized an infinite product formula posed by Wilf as a problem in American Mathematical Monthly, 1997. Chen and Choi established in 2013 two infinite product formulas, expressed in terms of the gamma function, whose special cases contain the above generalized infinite product formulas. In this paper, we generalize Chen and Choi's results.