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Mathematics of Computation

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

Author: Walter Gautschi
Journal: Math. Comp. 57 (1991), 309-324
MSC: Primary 65D32; Secondary 33C45, 44A10
MathSciNet review: 1079017
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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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Keywords: Slowly convergent series, Laplace transformation, summation by quadrature, Gaussian quadrature, orthogonal polynomials
Article copyright: © Copyright 1991 American Mathematical Society