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Mathematica HowTo
How to | Compute a Power Series
Calculus lets you approximate complicated functions with power series. Mathematica lets you generate and work with power series for a huge range of functions.
Use Series to make a power series out of a function. The first argument is the function. The second argument has the form {var, pt, order}, where var is the variable, pt is the point around which to expand, and order is the order:
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The "big-O" notation O[x]6 indicates that terms beyond x5 are omitted:
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Truncate the series to get a polynomial of degree 5 using Normal:
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At x=1., compare the polynomial and the original exponential function:
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