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Mathematica 10.3.0 was announced yesterday. This is the 6th release of Mathematica 10 during 16 months. I wonder its  MathematicaFunctionData and   FindFormula . At first sight, the former is an analog of FunctionAdvisor of Maple, but the latter isn't any analog. Also compare the outputs of

Residue[Binomial[n,k],{n,-j}]

(-1)^j/(j!*k!*(-j-k)!)

 and

>`assuming`([residue(binomial(n, k), n = -j)], [integer, j > 0]);

                residue(binomial(n, k), n = -j)
Let us wait for Maple 2016.

 
mathematica residue

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