21. Asymptotic expansions of angular prolate spheroidal wave functions for large values of c have been derived by M�ller.22. Several of his works have become classics, including " Matched Asymptotic Expansions : Ideas And Techniques ". 23. Asymptotic expansions of angular oblate spheroidal wave functions for large values of c have been derived by M�ller.24. The famous Feynman graphs in quantum field theory are another example of asymptotic expansions which often do not converge. 25. The relation between asymptotic expansions of spheroidal wave functions and Legendre functions has been investigated in M�ller and M�ller. 26. This is a typical example of the fact that Borel summation will sometimes " correctly " sum divergent asymptotic expansions . 27. It is often desirable to find more terms in the asymptotic expansions of both the outer and the inner solutions. 28. In general, the power series will not converge but will provide only an asymptotic expansion of the exact solution. 29. Detailed understanding of non-linear thread behavior requires the use of asymptotic expansions to generate the appropriate scaling behavior. 30. The absolute minimum value of the functional is then and the coefficient in the asymptotic expansion of } } } } is.
