Concerning the eigenvalues of a differential equation in convective heat transfer
An approximate value of X was obtained in the above cited paper by expanding "/" in a power series in y. Unfortunately, such an expansion is too slowly convergent to give a good estimate of X with only a limited number of terms. However, if the function / is expanded as a power series in the eigenvalue X, a much better value can be obtained with an equivalent number of terms. The means of obtaining such a series is quite simple and in fact a well known method, although its application to eigenvalue problems does not appear to have received the attention which would seem warranted in view of its utility as a means of obtaining numerical results. A more convenient form of the equation for this method is obtained by setting y = it + l)/4. Denoting derivatives with respect to by primes, the new equation is