juninho_ras
New member
- Joined
- Jun 7, 2017
- Messages
- 2
I have one definite integral that needs to be evaluated from -1 to 1 in the Cauchy principal value sense. Math programs only let me put the singular points between the integration limits , but my singular point is -1.
The integral is complex,it has a strong singularity on -1, but how can I integrate from -1 to 1?
Here is the function for simple copy and paste:
-(((1 - xi)*xi*Sqrt[(0.056249999999999994*(1 - xi) + 0.10625000000000001*xi - 0.049999999999999996*(1 + xi))^2]*
(0. + ((0.056249999999999994*(1 - xi) + 0.10625000000000001*xi - 0.049999999999999996*(1 + xi))*(-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))*
(1.3 + 4*(BesselK[0, 628.318530717959*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]] +
(0.003183098861837905*(-(0.0015915494309189525/Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]) +
BesselK[1, 628.318530717959*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]]))/
Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2])))/(Sqrt[(0.056249999999999994*(1 - xi)
+ 0.10625000000000001*xi - 0.049999999999999996*(1 + xi))^2]*
Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]) + (0.*(-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))*
(0.7 + 1256.637061435918*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]*
BesselK[1, 628.318530717959*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]] +
8*(BesselK[0, 628.318530717959*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]] +
(0.003183098861837905*(-(0.0015915494309189525/Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]) +
BesselK[1, 628.318530717959*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]]))/
Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2])))/(Sqrt[(0.056249999999999994*(1 - xi)
+ 0.10625000000000001*xi - 0.049999999999999996*(1 + xi))^2]*
Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2])))/(8*Pi*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]))
Does anyone has a hint on how to integrate the above function from -1 to 1 ?
The integral is complex,it has a strong singularity on -1, but how can I integrate from -1 to 1?
Here is the function for simple copy and paste:
-(((1 - xi)*xi*Sqrt[(0.056249999999999994*(1 - xi) + 0.10625000000000001*xi - 0.049999999999999996*(1 + xi))^2]*
(0. + ((0.056249999999999994*(1 - xi) + 0.10625000000000001*xi - 0.049999999999999996*(1 + xi))*(-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))*
(1.3 + 4*(BesselK[0, 628.318530717959*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]] +
(0.003183098861837905*(-(0.0015915494309189525/Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]) +
BesselK[1, 628.318530717959*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]]))/
Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2])))/(Sqrt[(0.056249999999999994*(1 - xi)
+ 0.10625000000000001*xi - 0.049999999999999996*(1 + xi))^2]*
Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]) + (0.*(-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))*
(0.7 + 1256.637061435918*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]*
BesselK[1, 628.318530717959*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]] +
8*(BesselK[0, 628.318530717959*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]] +
(0.003183098861837905*(-(0.0015915494309189525/Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]) +
BesselK[1, 628.318530717959*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]]))/
Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2])))/(Sqrt[(0.056249999999999994*(1 - xi)
+ 0.10625000000000001*xi - 0.049999999999999996*(1 + xi))^2]*
Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2])))/(8*Pi*Sqrt[0. + (-0.1 - 0.05*(1 - xi)*xi + 0.10625*(1 - xi)*(1 + xi) + 0.05625*xi*(1 + xi))^2]))
Does anyone has a hint on how to integrate the above function from -1 to 1 ?