Convolution product between x² and x³

[Jhenrique]

I tryied make the convolution product between x² and x³ by $\int_{- \infty}^{+ \infty} f(u) g(x-u) du$ and the result is an indeterminate form, however, by definition $\int_{0}^{x} f(u) g(x-u) du$, the result is 1/60 x⁶. So, $$\int_{- \infty}^{+ \infty} f(u) g(x-u) du \overset{?}{=} \frac{1}{60} x^6$$ ?

 

[Mark44]

I tryied make the convolution product between x² and x³ by $\int_{- \infty}^{+ \infty} f(u) g(x-u) du$ and the result is an indeterminate form, however, by definition $\int_{0}^{x} f(u) g(x-u) du$, the result is 1/60 x⁶. So, $$\int_{- \infty}^{+ \infty} f(u) g(x-u) du \overset{?}{=} \frac{1}{60} x^6$$ ?

Show us what you did, please.

 

[Jhenrique]

Show us what you did, please.

BTW, exist a symmetric algebraic definition for convolution where the graphic of the function f(x) is moved oppositely to g(x) and vice-versa (different of the standard definition, where a function is fixed and the another is moved over the first)? I tryied $\int_{- \infty}^{+ \infty} f(\frac{1}{2}x+u) g(\frac{1}{2}x-u) du$, but this expression isn't equal to the convolution of f and g...

 

[micromass]

I tryied make the convolution product between x² and x³ by $\int_{- \infty}^{+ \infty} f(u) g(x-u) du$ and the result is an indeterminate form, however, by definition $\int_{0}^{x} f(u) g(x-u) du$, the result is 1/60 x⁶.

OK, so far.

According to you, how does this follow exactly:

So, $$\int_{- \infty}^{+ \infty} f(u) g(x-u) du \overset{?}{=} \frac{1}{60} x^6$$ ?

 

[Jhenrique]

$$\int_{- \infty}^{+ \infty} f(u) g(x-u) du \overset{?}{=} \frac{1}{60} x^6$$

According to you, how does this follow exactly:

This equation isn't an affirmation, is a question. In acctually, I'm asking if $\int_{- \infty}^{+\infty} f(u)g(x−u)du$ is equal to $\int_{0}^{x} f(u)g(x−u)du$.

 

[micromass]

This equation isn't an affirmation, is a question. In acctually, I'm asking if $\int_{- \infty}^{+\infty} f(u)g(x−u)du$ is equal to $\int_{0}^{x} f(u)g(x−u)du$.

I know it's a question. But you're not going to learn much if we solve the question for you. So again, why do you think it's equal? Try to give the proof you're thinking of.