The classical Blasius boundary layer problem in its simplest statement consists in finding an initial value for the function satisfying the Blasius ODE on semi-infinite interval such that a certain condition at infinity be satisfied. Despite an apparent simplicity of the problem and more than a century of effort of numerous scientists, this elusive constant is determined at present numerically and not much better than it was done by Töpfer in 1912. Here we find this (Blasius) constant rigourously in closed form as a convergent series of rational numbers. Asymptotic behaviour, and lower and upper bounds for the partial sums of the series are also given.

Keywords:

Blasius problem, Crocco equation, rational approximations, acceleration of convergence