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The second Remes algorithm is used to approximate the integrals K& by rational functions. The related coefficients for the approximations of Kil, K&, K& are given for different precisions.The aim of this paper is to give rational-type approximations to the Bessel function integrals Ki,. The second Remes algorithm [7, 10] is employed and a class of rational functions which converges uniformly to the best approximation is used.The possibility of obtaining such a family and related theorems of convergence and existence are described in Is].

Two aspects of an iterative k-th-order procedure for solving equationsa) In the case where /(z) is a polynomial, the k-th-order method defines at each iteration a circle containing at least a zero of the polynomial. b) Each iteration function, when modified by introducing one parameter 2, has a descent property in the large, i.e. a$0>O can be found such that for 0 < 2 ~ 20: [1 (oJ~)[ < [/(z)], coa being the value of the iteration function at z and 2.

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