On the compilation of subscripted variables

where z = x -tiy, and the phase of z must be assigned, to make the logarithm single valued. The functions yn(z ) , n = 2, 3, . . may now be obtained from the usual recurrence relation. Preliminary tests of these formulas on the I B M 704 give results which compare favorably, both in speed and accuracy, with those obtained using convergent and asymptot ic series in the complex plane. If the real and imaginary parts of any of the functions are of different order of magnitude, the smaller component gives fewer significant figures (effectively the same number of decimal digits), but outside these regions at least seven significant figures were obtained, within the limits of the tables for J0 , J1 and Y0, Y1 published by the National Bureau of Standards (1 z[ =< 10).