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MathGroup Archive 1993

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Re: MMA Integration Warnings

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: MMA Integration Warnings
  • From: bert at netcom.com (Roberto Sierra)
  • Date: Thu, 18 Nov 1993 09:50:14 -0800

Roberto Sierra (bert at netcom.com) wrote:
:  	  +1
:  	 _
:  	/ i
:  	i
:  	 i
:  	  i	   -0.98     -0.98
:  	   i  (1-x)	(1+x)	   dx 
:   	   i
:  	i_/
:  	 
:  	 -1

Thanks to everyone who wrote in regarding this integral.  A couple
of folks have already pointed out that there was a bug in MMA v2.03
which appears to have been fixed in MMA v2.2, so now the answers
returned by Integrate and NIntegrate agree.  Thanks for such rapid
replies!!

	In[1]:= f[x_] := (1-x)^(-98/100) (1+x)^(-98/100)

	In[2]:= g = Integrate[f[x],{x,-1,1}]

	                       1
	        Sqrt[Pi] Gamma[--]
	                       50
	Out[2]= ------------------
	                  13
	            Gamma[--]
	                  25

	In[3]:= N[%]

	Out[3]= 51.3728

	In[4]:= NIntegrate[f[x],{x,-1,1}]

	NIntegrate::ncvb: 
	   NIntegrate failed to converge to prescribed accuracy after 7
	     recursive bisections in x near x = -1..

	Out[4]= 51.3739


This answer looks correct.


 \\|//                         "Television is a medium -- it is
  - -                           neither rare nor well done."
  o o                                            -- Ernie Kovacs
   J   roberto sierra
   O   tempered microdesigns    NOTICE:
  \_/  san francisco, ca        The ideas and opinions expressed
       bert at netcom.com          herein are not those of the author.





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