A class of slowly convergent series and their summation by Gaussian quadrature

Gautschi, Walter

doi:10.1090/S0025-5718-1991-1079017-5

A class of slowly convergent series and their summation by Gaussian quadrature
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Math. Comp. 57 (1991), 309-324 Request permission

Abstract:

Series are considered whose general term is a rational function multiplied by a fractional power. The summation of such series is reduced, via Laplace transformation techniques, to a problem of quadrature, which is then solved by Gaussian quadrature relative to Einstein and Fermi weight functions. A number of examples are worked out in detail.

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