Let be an analytic function f(x,y) so we want to take its Taylor series, my question is if we can do this:(adsbygoogle = window.adsbygoogle || []).push({});

-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)

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# Taylor series

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