An integral representation for the modified Bessel function of the third kind, computable for large, imaginary order

i erfc z and i2 erfc z correct to 6 significant figures (7 s.f. for z > 1) using single precision on a computer with word length of 8 decimal places, for all z for which e-z can be calculated correctly. To obtain greater accuracy, it is necessary either to use double precision or to use more than two different expansions for each function. From Gautschi's formula [2] for the number of terms required for calculation by backward recurrence, we see that that method will be better (for 7 s.f. accuracy) if all the z's of interest are greater than about 2.5. The advantage accruing from the use of Chebyshev approximations would be still greater for multiple-precision calculations of very high accuracy.