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

**References**:**Singularities at end point in integrations...***From:*ashesh <ashesh.cb@gmail.com>