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

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Discussion Overview

The discussion focuses on computing a Taylor expansion for a function of two variables, f(x,y), using Mathematica. Participants explore the syntax and interpretation of the output generated by the software.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant requests guidance on how to compute a Taylor expansion for f(x,y) in Mathematica.
  • Another participant suggests using the command Series[f[x,y],{x,0,1},{y,0,1}] to perform the expansion.
  • A participant expresses confusion over receiving terms like 0(y+2)^2 in the output and questions whether these terms are truly zero.
  • Another participant clarifies that the notation O[y+2]^2 represents higher order terms and is not the number zero, suggesting the use of Normal[Series[...]] to simplify the output.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the zero terms in the output, as some express confusion while others provide clarification. The discussion remains unresolved regarding the handling of these terms.

Contextual Notes

Participants have not fully addressed the implications of the notation used in the output, and there may be assumptions about the definitions of terms that are not explicitly stated.

chinaman209
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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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