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Math Help - Homogenous function

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by champrock View Post
    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 f(\lambda x) = \lambda^nf(x), which in your case, because of the expontential is zero. Now for your integral what you want

     <br />
\int_0^{\sqrt{x_1^2+x_2^2}} e^{-w^2/(x_1^2+x_2^2)}dw<br />

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

     <br />
r \int_0^1 e^{-y^2}dy = \frac{r \sqrt{\pi}}{2}\, \text{erf(1)}<br />
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  3. #3
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    can u please tell me what is the answer? I am getting "Homogeneous of degree 1". is that correct?

    thanks
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  4. #4
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    danny arrigo said

    A function is homogeneous of degree n if 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!)
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  5. #5
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