  We consider saddle point integrals in d variables whose phase function is
neither real nor purely imaginary. Results analogous to those for Laplace (real
phase) and Fourier (imaginary phase) integrals hold whenever the phase function
is analytic and nondegenerate. These results generalize what is well known for
integrals of Laplace and Fourier type. The method is via contour shifting in
complex d-space. This work is motivated by applications to asymptotic
enumeration.
