An incomplete Riemann zeta-function
is examined, along with a complementary incomplete Riemann zeta-function
. These functions are defined by
is the classical Riemann zeta function.
has the property that
. The asymptotic behaviour of
is studied for the case
, and using Liouville-Green (WKBJ) analysis, asymptotic approximations are obtained, complete with explicit error bounds, which are uniformly valid for