pitfall in analytic function
- To: mathgroup at smc.vnet.net
- Subject: [mg41411] pitfall in analytic function
- From: "Narasimham G.L." <google.news.invalid at web2news.net>
- Date: Sun, 18 May 2003 05:03:26 -0400 (EDT)
- Reply-to: "Narasimham G.L." <mathman-2oospam18 at hotmail.com>
- Sender: owner-wri-mathgroup at wolfram.com
I tried to integrate a transcendental function having factor (x-2),
analytic on the whole line, even at x=2, but unable to get through with
the smooth function at x=2.The following Mathematica prgram was run, and
although at x=2 it is a smooth plot ( minimum value is around -1.204 at
x=2.1), it proves to be a stumbling block in performing integration.
Plot [ (2^x-x^2)/(x-2), { x,0,4 }]
y1=Integrate [(2^x-x^2)/(x-2),{x,0,x}]
Plot[y1 ,{x,0, 4} ];
y2= -2 x - x^2/2 + 4 ExpIntegralEi[-2 Log[2] + x Log[2]] -
4 (ExpIntegralEi[-2 Log[2]] - Log[2]) - 4 Log[2 - x];
Plot[y2 ,{x,2.1, 4} ];
Plot[y2 ,{x,0, 4} ];
All integrates terminate at x=2. I like to treat a smooth analytic
continuous function in the normal way. Failure to do so negates
smoothness, continuity and analyticity, it would appear. How to
circumvent this problem?
Thanks for suggestions to overcome this problem.
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