The propagation characteristics of the radio wave were analyzed in a nonuniform atmosphere in which there exist an inverted layer with an even power profile of a height under a standard atmosphere and the lowest layer with a linear profile. If the modified index of refraction obtained by introduction of the earth-flattening approximation has a 2n power profile of the height, the solution of the wave equation cannot be given by a closed form function. Hence, the rigorous solution was obtained by a series representation in accordance with the method by Frobenius. This series solution is found effective even if the wave equation has two turning points close to each other. The function value can be obtained within a time shorter than the one required for the numerical solution such as the one by the Runge-Kutta method.By continuation of the analytic solutions for each atmospheric model layer, the wave function was derived and the received electric field at a far distance was obtained by the mode theory. It was found that the received electric field depends strongly on the order n of the 2n-th power N profile as the atmospheric layer near the zero of the index of refraction slope is increased.