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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 ofdoi:10.15439/2018f107 dblp:conf/fedcsis/Brzezinski18 fatcat:xqqlwl2i3zdg7pdrsghqix2zum