The response of a thermal reactor to a ramp change of reactivity is studied. When a single group of delayed neutrons is assumed, the differential equations for the time dependence of the thermal neutron flux takes the form of a linear homogeneous differential equation of the second order with linear coefficients, linearly independent solutions of the differential equation are found in the form of contour integrals. Moreover, expansions of these contour integrals into usable asymptotic developments are determined. Application of the mathematical results obtained is made to the problem of control rod calibration during a xenon transient.