BOOK REVIEWS IVol. XI, No. 2 3. The asymptotic series. For practical purposes, it is however advantageous to give up the convergence of the expansion and turn it into an ordinary divergent asymptotic series with simpler terms to be used for z » 1. To that end, one puts sinh 2 ~ cosh z e'/2, neglects the second term between the brackets in (2, 4), inserts the formulae given for Is+W2(z) into (2, 4) and rearranges the terms with respect to decreasing powers of z. Then one obtains