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A method to obtain fractional approximations to the Bessel function J0(x) is reported here. This method improves a recently published one principally in that all the parameters are uniquely determined by linear equations. Our approximations give fairly good accuracy for all real, positive values. The maximum absolute error for the first-degree approximation is about 0.0035, and for the fourth-degree one, about 2.8×10−6.
Antonio L. Guerrero (1985) studied this question.