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Re: CauchyPrincipalValue questions

• To: mathgroup at smc.vnet.net
• Subject: [mg69715] Re: CauchyPrincipalValue questions
• From: dh <dh at metrohm.ch>
• Date: Thu, 21 Sep 2006 07:30:44 -0400 (EDT)
• References: <eeof5i$23f$1@smc.vnet.net> <eeqqtl$oro$1@smc.vnet.net>

Hi Dimitri,
1) All the info I have lead to the conclusion that the x's come from 
CauchyPrincipalValue and not from NIntegrate.
2) It is not so astonishing that NIntegrate needs many more point than 
CauchyPrincipalValue. NIntegrate tries hard to integrate the steep 
increase near -eps. CauchPrincipalValue however already knows that we 
have a first order pole  and can use this info.
3) Neither NIntegrate nor CauchyPrincipalValue have the attribute 
"Listable". Therefore, you should not be able to give a List-argument. 
Therefore, that this works nevertheless with NIntegrate is astonishing, 
but it certainly does not work with CauchyPrincipalValue .E.g. instead, 
you could say:
CauchyPrincipalValue[#, {x, 0, {Pi/2}, 3*(Pi/4)}, AccuracyGoal -> 20]& 
/@ lst

Daniel