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11.5.5 Taylor Series

The a t (calc-taylor) [taylor] command computes a power series expansion or Taylor series of a function. You specify the variable and the desired number of terms. You may give an expression of the form ‘var = a’ or ‘var - a’ instead of just a variable to produce a Taylor expansion about the point a. You may specify the number of terms with a numeric prefix argument; otherwise the command will prompt you for the number of terms. Note that many series expansions have coefficients of zero for some terms, so you may appear to get fewer terms than you asked for.

If the a i command is unable to find a symbolic integral for a function, you can get an approximation by integrating the function's Taylor series.