Simple analytic approximations for the Blasius problem

• We derive analytic approximations for the Blasius function ff and its derivatives.
• We extend the integral iteration scheme for the Blasius problem devised by H. Weyl.
• We compute very accurate bounds for the second derivative of ff at the origin.
• We discuss the new approximations in the context of generalized Padè theory.

The classical boundary layer problem formulated by Heinrich Blasius more than a century ago is revisited, with the purpose of deriving simple and accurate analytical approximations to its solution. This is achieved through the combined use of a generalized Padé approach and of an integral iteration scheme devised by Hermann Weyl. The iteration scheme is also used to derive very accurate bounds for the value of the second derivative of the Blasius function at the origin, which plays a crucial role in this problem.