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A new series representation of the modified Bessel function of the second kind K0(x) in terms of simple elementary functions (Kummer’s function) is obtained. The accuracy of different orders in this expansion is analysed and has been shown not to be so good as those of different approximations found in the literature. In the sequel, new polynomial approximations for K0(x), in the limits 0 < x ≤ 2 and 2 ≤ x < ∞, are obtained. They are shown to be much more accurate than the two best classical approximations given by the Abramowitz and Stegun’s Handbook, for those intervals.

On new approximations for the modified Bessel function of the second kind \(K_0(x)\)