Analytic solutions of the Falkner-Skan equation when beta = -1 and gamma = 0

Two types of analytic solution for the Falkner-Skan equation are obtained when beta is -1 for the boundary conditions f(0) = gamma, f'(0) = 0, and f'(infinity) = 1. The first type is for the case when gamma is greater than or equal to the square root of 2, and is expressed in terms of exponential and error functions. It is essentially the same as that of Thwaites, but is obtained in a more direct way and present in more conventional notation. The second type is for the case when gamma is in the closed interval from 0 to 2, and is obtained in terms of confluent hypergeometric functions.