Recent content by csprh

So my stab at this. The original double integral is \int\limits_0^\infty\int\limits_0^\infty s_1 s_2 \exp\left(-\gamma \sqrt{s_1^2+s_2^2}\right) J_0\left(s_1r_1\right) J_0\left(s_2r_2\right) ds_1ds_2 Taking this one integral at a time (and extracting terms that need not be included in...

Hi Bill Sorry, this is my fault. I got the initial question wrong (see my second post). The mathematica code would be (from the corrected integral). in[1] := $Assumptions = {r1 > 0 && r2 > 0 && gamma > 0}; Integrate[ Integrate[ s1 s2 Exp[-gamma Sqrt[s1*s1 + s2*s2]] BesselJ[0, s1 r1]...

Jackmell I do understand that this forum is used by Maths undergrads to skip doing their homework. However, I'm a engineering postdoc who is completely hopeless at (this type of) maths and uses it as black box solutions. There's nobody in this department who works with this stuff so I...

Thanks Mandlebroth. I was looking at this and wondering how I could be so stupid not to see something so obvious. However noticing that \frac{\gamma}{\left(r_1^2+\gamma^2\right)^{3/2}} \times \frac{\gamma}{\left(r_2^2+\gamma^2\right)^{3/2}} \neq...

Hi I have proved (through educated guess-work and checking analytically) the following identity \int\limits_0^\infty\int\limits_0^\infty s_1 \exp\left(-\gamma s_1\right) s_2 \exp\left(-\gamma s_2\right) J_0\left(s_1r_1\right) J_0\left(s_2r_2\right) ds_1ds_2 =...

Hi all I have a univariate distribution of the form \frac{xγ}{((x^2+γ^2)^{1.5})} where both parameters are real and non-negative. How do I go about finding the bivariate form, where x and y (the new bivariate variables) are still both real and positive? To explain further what I mean, the...