Taylor series

 

In Axiom

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inputs outputs

    )set streams calculate 4

    series(%e**x, x = 0)

            1  2   1  3   1   4      5
    1 + x + - x  + - x  + -- x  + O(x )
            2      6      24
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)

    )set streams calculate 2

               2      3
    1 + 2x + 2x  + O(x )
                        Type: UnivariatePuiseuxSeries(Expression Integer,x,0)