# Homogenous function

• May 10th 2009, 04:02 AM
champrock
Homogenous function
Hello

The following function is homogenous of what degree?

f(x1,x2) : Integration of e^-{w^2/(x1^2+x2^2)} dw with limits from 0 to [x1^2+x2^2]^0.5

really lost in how to integrate this function and then find the required answer.
• May 10th 2009, 05:18 AM
Jester
Quote:

Originally Posted by champrock
Hello

The following function is homogenous of what degree?

f(x1,x2) : Integration of e^-{w^2/(x1^2+x2^2)} dw with limits from 0 to [x1^2+x2^2]^0.5

really lost in how to integrate this function and then find the required answer.

A function is homogneous of degree n if $\displaystyle f(\lambda x) = \lambda^nf(x)$, which in your case, because of the expontential is zero. Now for your integral what you want

$\displaystyle \int_0^{\sqrt{x_1^2+x_2^2}} e^{-w^2/(x_1^2+x_2^2)}dw$

If you let $\displaystyle y = \frac{w}{\sqrt{x_2^2+x_2^2}}$ and $\displaystyle r = \sqrt{x_2^2+x_2^2}$ then the integral becomes

$\displaystyle r \int_0^1 e^{-y^2}dy = \frac{r \sqrt{\pi}}{2}\, \text{erf(1)}$
• May 10th 2009, 06:00 AM
champrock
can u please tell me what is the answer? I am getting "Homogeneous of degree 1". is that correct?

thanks
• May 10th 2009, 06:44 AM
HallsofIvy
danny arrigo said

Quote:

A function is homogeneous of degree n if $\displaystyle f(\lamba x)= \lambda^n f(x)$, which in your case, because of the expontential, is zero.
(I seem to be following danny arrigo around!)
• May 10th 2009, 07:55 AM
Jester
Sometimes people just need to hear more than once! (Nod)