Series Representation of the Modified Bessel Function of the Second Kind $K_0(\beta x)$

Francisco Caruso, Felipe Silveira


A series representation of the modified Bessel function of the second kind $K_0(\beta x)$ in terms of simple elementary functions is obtained. Predictions corresponding to different orders in the expansion are compared with the original function together with an analysis of the corresponding errors. An alternative way of writing $K_0(\beta x)$ is given in terms of a confluent hypergeometric function.

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