On generalized Gaussian quadrature

Luke, Yudell L.; Ting, Bing Yuan; Kemp, Marilyn J.

doi:10.1090/S0025-5718-1975-0388740-8

On generalized Gaussian quadrature
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by Yudell L. Luke, Bing Yuan Ting and Marilyn J. Kemp PDF

Math. Comp. 29 (1975), 1083-1093 Request permission

Abstract:

A general interpolation formula is derived such that when it is multiplied by a weight function and integrated, the result becomes a generalized Gaussian quadrature scheme which allows for an arbitrary number of preassigned nodes. The errors in the interpolation and quadrature formulas are studied. All of this generalizes previous results of the first-named author where no preassigned nodes were permitted.

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The Special Functions and Their Approximations

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