Analytic Solutions of the Falkner–Skan Equation when β = - 1and γ = 0

Two types of unique analytic solution are presented for the Falkner–Skan equation f'''( η ) + ff'' + β ( 1 - ( f' )² ) = 0 when β = - 1, subject to the boundary conditions f( 0 ) = γ f'( 0 ) = 0,f'( ∞ ) = 1. For γ √2, f''( 0 ) = √γ ² - 2, the solution is given in terms of exponential and error functions, with f'( η ) in a dominantly exponential asymptotic approach to unity. For 0 γ √2 f''(0) = 0, the solution is given in terms of confluent hypergeometric functions, with an algebraic approach from above. As γ increases continuously from zero, the solution goes over continuously from an algebraic to a dominantly exponential approach through γ = √ 2.