Re: hi, how can i accomplish this densityplot?

• To: mathgroup at smc.vnet.net
• Subject: [mg107406] Re: [mg107392] hi, how can i accomplish this densityplot?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 11 Feb 2010 08:33:13 -0500 (EST)

```The problem is that you used patterns (e.g., x_) in the function in the DensityPlot.  You should also restrict the definition of f to numeric arguments since the RHS cannot evaluate without numeric input.

f[x_?NumericQ, y_?NumericQ] :=
NIntegrate[r0*Exp[-(r0 + 2*
(x^2 + y^2 + r0^2 + 2*r0*
((x^2 + y^2)^0.5)*
(Cos[theta0]*(y/(x^2 + y^2)^0.5) -
Sin[theta0]*(x/(x^2 + y^2)^0.5))
)^0.5)],
{r0, 0, Infinity}, {theta0, 0, Pi}]

DensityPlot[f[x, y], {x, -2, 2}, {y, -2, 2}]

Bob Hanlon

---- "=E7=9C=9F=E5=A5=BD=E5=91=BD" <hiphopphysics at yahoo.com.tw> wrote:

=============
f[x_, y_] :=
NIntegrate[
r0*Exp[-(r0 +
2*(x^2 + y^2 + r0^2 +
2*r0*((x^2 + y^2)^0.5)*(Cos[theta0]*(y/(x^2 + y^2)^0.5) -
Sin[theta0]*(x/(x^2 + y^2)^0.5)))^0.5)], {r0, 0,
Infinity}, {theta0, 0, Pi}]

DensityPlot[f[x_, y_], {x, -2, 2}, {y, -2, 2}]

i entered the code above but mathematica return the error message:

NIntegrate::inumr: The integrand E^(-r0-2 (r0^2+<<1>>+<<1>>+2 r0
Power[<<2>>] Plus[<<2>>])^0.5) r0 has evaluated to non-numerical
values for all sampling points in the region with boundaries {{\
[Infinity],0.},{0,3.14159}}. >>

General::stop: Further output of NIntegrate::inumr will be suppressed
during this calculation.