1. Actually, it is not necessary forgto be constant spacewise outside that portionRof the boundary where the defect is to be introduced.
2. An alternative method of solution for case (ii) is given by Titchmarsh,Introduction to the Theory of Fourier Integrals(Oxford University Press, London, 1937), pp. 337–339. The solution is obtained there as a particular case of a general method employing Mellin transforms.
3. Watson,Bessel Functions(Cambridge University Press, Cambridge, 1945), p. 405. We refer to this book as Watson henceforth.