[Date Index]
[Thread Index]
[Author Index]
Re: Singularities at end point in integrations...
*To*: mathgroup at smc.vnet.net
*Subject*: [mg64140] Re: [mg64104] Singularities at end point in integrations...
*From*: Pratik Desai <pdesai1 at umbc.edu>
*Date*: Thu, 2 Feb 2006 00:06:50 -0500 (EST)
*References*: <200602010934.EAA23064@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
ashesh wrote:
>Hi,
>
> I Need to perform an integration with poles and zeros in the integrand. Please let me know if there a way in Mathematican that can be used to perform the definite integral
>
> sqrt((x-a)*(x-b)/((x-c)*(x-d)))
>
>between the limits (c,d), (a,d), (a,b) or (b,c).
>
>I have read about the routine in quadpack called "dqawse.f" which can perform "integration of functions having algebraico-logarithmic end point singularities".
>
>
>Hope someone can give some leads to solve the above problem.
>
>Thanks in advance.
>Ashesh
>
>
>
Perhaps using the package <<NumericalMath`CauchyPrincipalValue`
Here is what I tried
In[333]:=
a=-1;
b=1;
c=-2;
d=2;
<<NumericalMath`CauchyPrincipalValue`
Integrate[((x-a)*(x-b)/((x-c)*(x-d)))//ExpandAll//Together//Sqrt,{x,a,b},PrincipalValue->True]//N//Chop
CauchyPrincipalValue[((x-a)*(x-b)/((x-c)*(x-d)))//ExpandAll//Together//Sqrt,
{x, a,{c},d}]
CauchyPrincipalValue[((x-a)*(x-b)/((x-c)*(x-d)))//ExpandAll//Together//Sqrt,
{x, a,{c},b}]
CauchyPrincipalValue[((x-a)*(x-b)/((x-c)*(x-d)))//ExpandAll//Together//Sqrt,
{x, b,{c},d}]
CauchyPrincipalValue[((x-a)*(x-b)/((x-c)*(x-d)))//ExpandAll//Together//Sqrt,
{x, b,{d},c}]
Out[338]=
0.812598
Out[339]=
0.812589\[InvisibleSpace]+1.34387 \[ImaginaryI]
Out[340]=
0.812598
Out[341]=
0.\[InvisibleSpace]+1.34385 \[ImaginaryI]
Out[342]=
-0.812589-1.34387 \[ImaginaryI]
Hope this helps
Pratik
Prev by Date:
**Re: Utilizing the Result From Solve[]**
Next by Date:
**Re: Re: Recommended learning exercises for beginners?**
Previous by thread:
**Singularities at end point in integrations...**
Next by thread:
**Re: Singularities at end point in integrations...**
| |