Laplace's Method

Another common case arises whenp(r) has a simple minimum at an interior point to of (a, b) and q(ro) # 0. Then

finite or infinite. The functions p( t ) and q ( t ) are independent of x , p ( t ) being real and q( t ) either real or complex. In addition:

(i) p( t ) > p(a) when t E (a, b), and for every c E (a, b) the infimum of p(t)-p(a) in [c, b) is positive.