In the paper there are presented efficient and accurate methods of Gauss-Jacobi nodes and weights computation. They include an enhancement for standard iteration method for Jacobi polynomials zeros finding, weight function formula transformation for increased accuracy of fractional derivatives computation and arbitrary precision application for mitigation of double precision arithmetic flaws. The results of numerical experiments presented in the paper prove high accuracy and efficiency of developed methods for computation of quadratures' nodes and weights, decreased amount of required iterations for polynomials zeros finding and elimination of truncation errors during weights computation. Accuracy of computations depends on height of precision applied for it, which is limited only by accessible hardware.
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