  The well-known astrophysical resonant reaction rate equations for an isolated
narrow resonance have been reexamined. The validity of those `look reliable'
assumptions used in deriving the analytic reaction rate equations has been
checked, and the reality is they only hold for certain circumstances.
Importantly an integration-range issue hidden in the classical integration
equations has been revealed and it hints us not to use those analytic equations
in the future. This work may influence all those work in which the classical
narrow resonant equations were used for calculating the stellar reaction rates,
especially at low stellar temperatures, and may affect the results of stellar
evolution and nucleosynthesis network calculations considerably.
