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Fast summation methods based on quadratures of Gaussian type
Last modified: 2014-02-20
Abstract
An account on summation/integration metfods for computation of slowly convegent series and finite sums are given. Methods are based on Gauss quadrature formulas with respect to some nonclassical weight functions over real (half) line. A recent progress in symbolic computation and variable-precision arithmetic are used in the construction of such quadrature rules. Some interesting special cases are presented.
Keywords
Summation; Gaussian quadrature; weight function; convergence