Expansions over a Simplex of Real Functions by Means of Bernoulli Polynomials
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In  there is an expansion in Bernoulli polynomials for sufficiently smooth real functions in an interval [a,b]⊂R that has useful applications to numerical analysis. An analogous result in a 2-dimensional context is derived in  in the case of rectangle. In this note we generalize the above-mentioned one-dimensional expansion to the case of Cm-functions on a 2-dimensional simplex; a method to generalize the expansion on an N-dimensional simplex is also discussed. This new expansion is applied to find new cubature formulas for 2-dimensional simplex.
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