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Solving the distribution function

  1. Jul 25, 2011 #1
    I want to solve following double integration. I am stuck from long time. Any intermediate solution will also be appreciated.

    [itex]\int[/itex][itex]\int[/itex] dvb dvl (feven+fodd)


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

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

    Where, [itex]\eta[/itex], 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 -[itex]\sqrt{2*potential - vb[itex]^{2}[/itex] - vr[itex]^{2}[/itex]}[/itex]<=vl<=[itex]\sqrt{2*potential - vb[itex]^{2}[/itex] - vr[itex]^{2}[/itex]}[/itex] and -[itex]\sqrt{2*potential - vr[itex]^{2}[/itex]}[/itex]<=vb<=[itex]\sqrt{2*potential - vr[itex]^{2}[/itex]}[/itex]

    Also -3.5< =[itex]\beta[/itex] <1
    and 0<= [itex]\eta[/itex] <=2
    Any help will be highly appreciated
  2. jcsd
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