ABSTRACT
Finally, we displace the paths for the inner integrals into the lines Imo = +n and Im o = -4n, respectively, and then refer to equation (8.03) of Chapter 7. Thus we arrive at Nicholson's integral:
8 Nv (r ) Po (2z sinh w) cosh (2vw) dw. (7.01)
Although the foregoing derivation can be placed on a sound footing, the analysis is difficult.' Instead, following Wilkins (1948) we shall verify the suggested result by quite a different method. 7.2 Theorem 7.1 The integral (7.0 1 ) converges when I ph zl< +n and equals J,? ( z ) + Y,? ( z ) .
