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