On some conjectures of Askey

Using the Darboux method of asymptotic analysis, it is shown that the coefficients of the power series expansions of the functions f(w)=(1−w)^−c(1−2xw+w²)^−c and (1+w)f(w), 1<c<2, at w=0 are positive if x lies in certain intervals. This partially answers some questions raised by Askey.