Generating functions for newton-cotes formulae weights and error terms

Abstract

From the observation that weights in the Newton-Cotes formulae look like integrals of binomial coefficient polynomials, we are able to evaluate their generating function. We also obtain a generating function for the error terms in the Newton-Cotes formulae by generalizing the Euler-Maclaurin sum formula.

Keywords:

• Newton-Cotes
• Euler-MacLaurin
• generating function
• quadrature

AMS:

• 65D32
• 05A15
• 65B15

^†Supported by a Fannie and John Hertz Foundation Fellowship

^†Supported by a Fannie and John Hertz Foundation Fellowship

Notes

^†Supported by a Fannie and John Hertz Foundation Fellowship

Additional information

Notes on contributors

Bradley W. Brock

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