# Computing area below 2D function

I'm trying to find an area (in η and y plane) in which the below function is >=0

-1. η ((-5. + y) MeijerG[{{-0.5}, {}}, {{0., 0.}, {-1.}}, y^2]
+ (10. - 2. y) MeijerG[{{-0.5}, {}}, {{0., 0.}, {-1.}}, 4. y^2]
+ 2. MeijerG[{{-0.5}, {}}, {{0., 1.}, {-1.}}, y^2]
- 4. MeijerG[{{-0.5}, {}}, {{0., 1.}, {-1.}}, 4. y^2])


Why doesn't RegionPlot doesn't work?

The code is:

RegionPlot[-1. η ((-5. + y) MeijerG[{{-0.5}, {}}, {{0., 0.}, {-1.}}, y^2] + (10. - 2. y) MeijerG[{{-0.5}, {}}, {{0., 0.}, {-1.}}, 4. y^2] + 2. MeijerG[{{-0.5}, {}}, {{0., 1.}, {-1.}}, y^2] - 4. MeijerG[{{-0.5}, {}}, {{0., 1.}, {-1.}}, 4. y^2])>0,{y,0,5},{η,0,0.01}]

• What is the full code here...? – ktm Nov 30 '18 at 17:48
• Immediately I can see that this might not work because when y=0, this is undefined and an error occurs. You say it "doesn't work", what exactly is going wrong for you? – wilsnunn Dec 1 '18 at 12:58
• It takes a long time and then the kernel quits – Perfect Fluid Dec 1 '18 at 17:36

The required area can be calculated as follows.

NIntegrate[ Boole[-1. \[Eta] ((-5. + y) MeijerG[{{-0.5}, {}}, {{0., 0.}, {-1.}},
y^2] + (10. - 2. y) MeijerG[{{-0.5}, {}}, {{0., 0.}, {-1.}},
4. y^2] + 2. MeijerG[{{-0.5}, {}}, {{0., 1.}, {-1.}}, y^2] -
4. MeijerG[{{-0.5}, {}}, {{0., 1.}, {-1.}}, 4. y^2]) > 0], {y,0,5}, {\[Eta], 0, 0.01}, AccuracyGoal -> 3]


0.0197613

Here is a picture

created by

Plot3D[{-1.*\[Eta]*((-5. + y) MeijerG[{{-0.5}, {}}, {{0., 0.}, {-1.}},
y^2] + (10. - 2. y) MeijerG[{{-0.5}, {}}, {{0., 0.}, {-1.}},
4. y^2] + 2. MeijerG[{{-0.5}, {}}, {{0., 1.}, {-1.}}, y^2] -
4. MeijerG[{{-0.5}, {}}, {{0., 1.}, {-1.}}, 4. y^2]), 0}, {y, 0, 5}, {\[Eta], 0, 0.01}]