论文信息 - A class of slowly convergent series and their summation by Gaussian quadrature

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

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.

Walter Gautschi | W. Gautschi

[1] M. K. Kerimov,et al. Applied and computational complex analysis. Vol. 1. Power series, integration, conformal mapping, location of zeros: Henrici P. xv + 682 pp., John Wiley and Sons, Inc., New York — London, 1974☆ , 1977 .

[2] W. J. Cody,et al. Chebyshev approximations for the Fresnel integrals , 1968 .

[3] Walter Gautschi,et al. Gaussian quadrature involving Einstein and Fermi functions with an application to summation of series , 1985 .

[4] Henry C. Thacher,et al. Applied and Computational Complex Analysis. , 1988 .

[5] Kathleen A. Paciorek,et al. Chebyshev approximations for Dawson’s integral , 1970 .

[6] Walter Gautschi,et al. Computational Aspects of Orthogonal Polynomials , 1990 .