question

**alejandrito29** · Nov26-09, 02:05 PM

i need to integrate

LaTeX Code: -(p(y)f(y)single-quote)single-quote=m^2w(y)f(y)

where
$LaTeX Code: p(y)=e^{4ky}(1-4ak^2)$ and $LaTeX Code: w=-4ae^{2y}k\\delta(y)$

but y between [0,infinity[

¿i calculate between $LaTeX Code: \\int^{epsilon}_0????$ or ¿i calculate between [-epsilon,epsilon]?????

but, what is??

$LaTeX Code: \\int^{\\epsilon}_0(p(y)f(y)single-quote)single-quotedy$

whit f is not continuous in zero

the result is
$LaTeX Code: f(+\\epsilon)=-\\frac{m^24akf(0)}{1-4ak^2}$

**HallsofIvy** · Nov26-09, 08:49 PM

Originally Posted by alejandrito29

i need to integrate

where
$LaTeX Code: p(y)=e^{4ky}(1-4ak^2)$ and $LaTeX Code: w=-4ae^{2y}k\\delta(y)$

but y between [0,infinity[

¿i calculate between $LaTeX Code: \\int^{epsilon}_0????$ or ¿i calculate between [-epsilon,epsilon]?????

I have no idea what you are talking about. What are yu integrating? If you are talking about the integral above, if it is given as a definite integral, you use whatever limits of integration are given. If it is given as an indefinite integral (anti-derivative) you do not use any limits of integration.

but, what is??

$LaTeX Code: \\int^{\\epsilon}_0(p(y)f(y)single-quote)single-quotedy$

By the Fundamental Theorem of Calculus, the integral of the derivative of any function is that function:
$LaTeX Code: \\int^{\\epsilon}_0(p(y)f(y)single-quote)single-quotedy= p(y)f(y)single-quote$

whit f is not continuous in zero

If f is not continuous at zero, then it is not differentiable at zero and the integrand above does not exist at 0.

the result is
f(+\epsilon)=-\frac{m^24akf(0)}{1-4ak^2}

Since you haven't actually stated what the problem is, I have no idea whether that is correct or not.

**alejandrito29** · Nov26-09, 10:39 PM

Originally Posted by HallsofIvy

Since you haven't actually stated what the problem is, I have no idea whether that is correct or not.

$LaTeX Code: f(+\\epsilon)=-\\frac{m^24akf(0)}{1-4ak^2}$
this problem is in eq. (3)-(6)......(10)
of:
http://arxiv.org/PS_cache/hep-th/pdf/0311/0311267v3.pdf