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On Birkhoff quadrature formulas

Author: A. K. Varma
Journal: Proc. Amer. Math. Soc. 97 (1986), 38-40
MSC: Primary 41A55
MathSciNet review: 831383
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Abstract: In an earlier work the author has obtained new quadrature formulas (see (1.3)) based on function values and second derivatives on the zeros of $ {\prod _n}\left( x \right)$ as defined by (1.2). The proof given earlier was quite long. The object of this paper is to provide a proof of this quadrature formula which is extremely simple and indeed does not even require the use of fundamental polynomials of (0,2) interpolation.

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