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21, ... , 100 were computed by use of the "asymptotic" expansion given in (5). The "overlap" of the two methods for n = 20, 21, * * *, 25 was provided as a numerical verification of this "asymptotic" expansion. It was found that these two methods, gave results which differed (in the eighth significant digit) by thirteen units for n = 20, four units for n = 21, and not more than one unit for n = 22, 23, 24, and 25. Since the numerical integrations were computed in an ascending order, i.e., the integrand for Mn(') was multiplied by t in order to obtain the integrand for M(l)l, n = 2, 3, ... , 24, and, in view of the agreement indicated above, it is felt that all values in Table 2 are correct, except for possible rounding errors of one unit in the eighth significant digit.

Bessel-function identities needed for the theory of axisymmetric gravity waves