- #1
Karlisbad
- 131
- 0
Let be an analytic function f(x,y) so we want to take its Taylor series, my question is if we can do this:
-First we expand f(x,y) on powers of y considering x a constant so:
[tex] f(x,y)= \sum_{n=0}^{\infty}a_{n} (x)y^{n} [/tex]
and then we expand a(n,x) for every n into powers of x so we have..
[tex] f(x,y)= \sum_{n=0}^{\infty}\sum_{m=0}^{\infty}b_{n}x^{m} y^{n} [/tex]
I don't know if the result will be the same that taking the "Double Taylor series " for the function f(x,y)
-First we expand f(x,y) on powers of y considering x a constant so:
[tex] f(x,y)= \sum_{n=0}^{\infty}a_{n} (x)y^{n} [/tex]
and then we expand a(n,x) for every n into powers of x so we have..
[tex] f(x,y)= \sum_{n=0}^{\infty}\sum_{m=0}^{\infty}b_{n}x^{m} y^{n} [/tex]
I don't know if the result will be the same that taking the "Double Taylor series " for the function f(x,y)