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Question: What shall I do if the function is two variable like f(x,y)=xy/(y−x*sqrt(y)−x^2) and intended to keep terms upto order 5.

Question:What shall I do if the function is two variable like f(x,y)=xy/(y−x*sqrt(y)−x^2) and intended to keep terms upto order 5.

pallav 90 Maple
series mtaylor taylor duplicate-question
August 21 2022
0

For a single variable function, I can expand the function 

series(x/(1−x−x^2),x,4);

and get the expansion upto order 4 term.

What shall I do if the function is two variable like f(x,y)=xy/(y−x*sqrt(y)−x^2) and intended to keep terms upto order 5, or moreseries.mw

series(x/(-x^2-x+1), x, 4)

series(x+x^2+2*x^3+O(x^4),x,4)

 (1)

series(series(x*y/(1-x*sqrt(y)-x^2), x, 8), y, 4)

O(x^8)+(x^7+x^5+x^3+x)*y+(3*x^6+2*x^4+x^2)*y^(3/2)+(6*x^7+3*x^5+x^3)*y^2+(4*x^6+x^4)*y^(5/2)+(5*x^7+x^5)*y^3+x^6*y^(7/2)+O(y^4)

 (2)

``

Download series.mw

say.

My attempt failed as (x^7 + x^5 + x^3 + x)*y etc contains O(8) terms x^7.y

Please help. 
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