I want to represent a function like f(x,y)=sin(1/(x+y)) about [x,y]=[0,0] in series type. how can i do it in matlab or maple?
Removable singularities and Laurent series usually do the trick, but your function is too pathological even for this methodology.
Hi Shahram Hosseini
I think no series expansion is available for sin(1/(x + y)) at [x, y] = (0, 0).
However, the series expansion is available at x = 0 such that y ≠ 0.
Removable singularities and Laurent series usually do the trick, but your function is too pathological even for this methodology.
You need Maclaurin's expansion with two valuables.
For example, see Eq. (4-6) and example in the following link, putting a=b=0
https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Multivariable_Calculus/3%3A_Topics_in_Partial_Derivatives/Taylor__Polynomials_of_Functions_of_Two_Variables
or see the equations and example in the following
https://pictblog.com/taymac-5
You can use Maclaurin's expansion using Matlab see this link https://www.mathworks.com/matlabcentral/answers/76106-maclaurin-series-function-in-matlab
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