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Re: How to do integration symbolically with cauchy principal values

• To: mathgroup at smc.vnet.net
• Subject: [mg65666] Re: [mg65636] How to do integration symbolically with cauchy principal values
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Wed, 12 Apr 2006 06:00:32 -0400 (EDT)
• References: <200604110804.EAA11309@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

simon yang wrote:
> Dear everyone,
> I meet a cauchy integration when calculating optical functions with
> Kramers-Kronig integration:
> \!\(\(ϵ\_1\) \((x)\) =
>         constant + \(2\/Ï?\) P \(â?«\_x0\%â??\(\( ξ*\(ϵ\_2\)
> \((ξ)\)\)\/\(ξ\^2 -
>          x\^2\)\) \[DifferentialD]ξ\)\)
> How to do it symbolically in Mathematica?
> And how to develope software with Mathematica with interfaces like VC++
> ?

Regarding your first question, I can't read your input, so I'll give a 
simple example instead:

In[1]:=
Integrate[1/x,{x,-2,1},PrincipalValue->True]

Out[1]=
-Log[2]

Carl Woll
Wolfram Research

• References:
  • How to do integration symbolically with cauchy principal values
    • From: "simon yang" <yanshanguke@163.com>