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

DOI:
https://doi.org/10.1090/S0025-5718-1991-1079017-5

MathSciNet review:
1079017

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1991-1079017-5

Keywords:
Slowly convergent series,
Laplace transformation,
summation by quadrature,
Gaussian quadrature,
orthogonal polynomials

Article copyright:
© Copyright 1991
American Mathematical Society