# Solving the distribution function

1. Jul 25, 2011

### astro_enthu

I want to solve following double integration. I am stuck from long time. Any intermediate solution will also be appreciated.

$\int$$\int$ dvb dvl (feven+fodd)

where,

feven = (r*(vl$^{2}$+vb$^{2}$))^(-2*$\beta$)*(potential - 0.5*(vl$^{2}$+vb$^{2}$+vr$^{2}$))^(-3*$\beta$+5.5), where $\beta$,potential and vr are some constant numbers

fodd = (1-$\eta$)*tanh(r*vl*cos(b)/1000)*feven

Where, $\eta$, r,b are constant numbers. Which means I want to marginalise (feven+fodd) over vl and vb.

Integration limits for vl and vb comes from energy equation. Limits are -$\sqrt{2*potential - vb$^{2}$ - vr$^{2}$}$<=vl<=$\sqrt{2*potential - vb$^{2}$ - vr$^{2}$}$ and -$\sqrt{2*potential - vr$^{2}$}$<=vb<=$\sqrt{2*potential - vr$^{2}$}$

Also -3.5< =$\beta$ <1
and 0<= $\eta$ <=2
Any help will be highly appreciated