Mathematica How to compute a Taylor expansion for f(x,y) using Mathematica?

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SUMMARY

The discussion focuses on computing a Taylor expansion for the function f(x,y) using Mathematica's Series function. The correct syntax is Series[f[x,y],{x,0,1},{y,0,1}]. Users encountered zero terms in their expansions, which were clarified as O(y+2)^2, indicating higher order terms rather than actual zeros. To eliminate these terms, the Normal function should be applied: Normal[Series[...]].

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Can someone pls explain hot to compute a taylor expansion for f(x,y) using mathematica
 
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Series[f[x,y],{x,0,1},{y,0,1}]
 
When I expand like that i get some zero terms like 0(y+2)^2.. and so one repeated a finite number of times. When i try to simplify the answer the zeroes don't go away. So are these really zero?
 
Those are not 0 (number zero) they are O (letter "Oh"). The term O[y+2]^2 means an unspecified term of order (y+2)^2 to represent all of the higher order terms in the expansion. If you want to get rid of it then just use:

Normal[Series[...]]
 

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