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- Here, I present a silly question about the notation of sums.

I have a doubt about the notation and alternative ways to represent the terms involved in sums.

Suppose that we have the following multivariable function,

$$f(x,y)=\sum^{m}_{j=0}y^{j}\sum^{j-m}_{i=0}x^{i+j}$$.

Now, let ##\psi_{j}(x)=\sum^{j-m}_{i=0}x^{i+j}##. In the light of the foregoing, is it correct to express ##f(x,y)## as follows

$$f(x,y)=\sum^{m}_{j=0}y^{j}\psi_{j}(x)$$ ?

Thanks in advance!

Suppose that we have the following multivariable function,

$$f(x,y)=\sum^{m}_{j=0}y^{j}\sum^{j-m}_{i=0}x^{i+j}$$.

Now, let ##\psi_{j}(x)=\sum^{j-m}_{i=0}x^{i+j}##. In the light of the foregoing, is it correct to express ##f(x,y)## as follows

$$f(x,y)=\sum^{m}_{j=0}y^{j}\psi_{j}(x)$$ ?

Thanks in advance!