WOLFRAM|DEMONSTRATIONS PROJECT

Asymptotic Expansions

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function to approximate
x!
SinIntegral[x]
number of terms
1
2
3
4
An asymptotic expansion of a function is an expression of that function as an infinite series of polynomial terms. A partial sum of that series is a polynomial that approximates the function with the approximation generally improving as more terms are used. For these two examples, as the number of terms increases, the error near
x=0
increases, yet the error for larger values of
x
decreases.