11. Evaluating both, one obtains the asymptotic expansion 12. This allows one to compute the asymptotic expansion 13. Boundary-layer theory is amenable to the method of matched asymptotic expansions for deriving approximate solutions. 14. The most common type of asymptotic expansion is a power series in either positive or negative powers. 15. I've read through asymptotic expansion , but didn't get anything out of it. 16. He is known for pioneering work in applying the method of asymptotic expansion to fluid mechanics problems. 17. Substituting the asymptotic expansion for each of the cosines into the spherical relation for a right triangle yields 18. The two solutions can then be matched with each other, using the method of matched asymptotic expansions . 19. Despite non-convergence, the asymptotic expansion is useful when truncated to a finite number of terms. 20. This way of optimally truncating an asymptotic expansion is known as "'superasymptotics " '.