semiclassical approximation for the exponential sum (partition function)

Question

for any real and positive 's' and in the sense of semiclassical approximation

is this valid ??

$ \sum_{n}exp(-sE_{n})\sim \iint_{C}dxdpe^{-s(p^{2}+V(x))}$ valid for every 's'

here simply both the sum and integral are convergent, so in this case the approximation can be seen as the replacement of a sum by an integral.