The tabulation of Bessel functions for large argument

Extract

By the use of an auxiliary independent variable, as well as of auxiliary functions, it may be possible to obtain tables which are very compact and in which, nevertheless, linear interpolation is adequate for most practical purposes. In the case of the Bessel functions of order zero, it is shown that by the use of 1/x² as auxiliary independent variable, and appropriate auxiliary functions, linear interpolation in two tables of forty-one entries each is sufficient to give x^½12J₀(x) and x^½12Y₀(x) with an uncertainty of a unit in the 7th decimal, from x = 5 to ∞, and two tables of only three values each are sufficient to cover the range x = 22·5 to ∞ in the same way. Two possible forms of auxiliary functions for this purpose are considered.