We perform an asymptotic evaluation of the Hankel transform, 
, for arbitrarily large 
of an entire exponential type function, 
, of type 
by shifting the contour of integration in the complex plane. Under the situation that 
has an odd parity with respect to 
and the condition that the asymptotic parameter is greater than the type , we obtain an exactly terminating Poincar{\’e} expansion without any trailing subdominant exponential terms. That is the Hankel transform evaluates exactly into a polynomial in inverse as approaches infinity.