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2.33.3  Series expansion : series

series takes from one to four arguments :

Note that the syntax ...,x,a,n,... (instead of ...,x=a,n,...) is also accepted.
series returns a polynomial in x-a, plus a remainder of the form:

(x-a)^n*order_size(x-a)

where order_size is a function such that,

∀ r>0,    
 
lim
x→ 0
 xr order_size(x) = 0 

The order returned by series may be smaller than n if cancellations between numerator and denominator occur.

Examples :


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