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A generalized version of the weighted-averages method is presented for the acceleration of convergence of sequences and series over a wide range of test problems, including linearly and logarithmically convergent series as well as monotone and alternating series. This method was originally developed in a partitionextrapolation procedure for accelerating the convergence of semiinfinite range integrals with Bessel function kernels (Sommerfeld-type integrals), which arise in computationaldoi:10.2528/pierm10100702 fatcat:xfpsvhq3e5daxn6gakdwsio6gq