Re: Problem with Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg25996] Re: Problem with Integrate
- From: Hendrik van Hees <h.vanhees at gsi.de>
- Date: Wed, 15 Nov 2000 02:09:46 -0500 (EST)
- References: <8ur14j$r05@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
This seems to be a bug of the same type I always posted in this group sometimes. I never got a sensible answer. The only message I got is that one has to be very careful when doing a definite integral over integrands which are multi-valued as complex functions. In your case the problem is again the square root. The only way out of this problem is the following procedure: (1) Use mathematica to get an indefinite integral (2) Check by differentiation if the result is correct (up to now I've not found a bug in indefinite integrals) (3) use analytic continuation techniques to define the result in the sheet you need it BY HAND. I've not found a solution with automatic calculations in Mathematica so far. Be sure to know Mathematica's conventions of the functions concerning branch cuts in the Riemann surface. (4) Use Mathematica to set in the boundary values of your integral in the corrected indefinite Integrand. (5) Define often needed functions in a separate notebook or package for quick use the next time ;-)). -- Hendrik van Hees Phone: ++49 6159 71-2751 c/o GSI-Darmstadt SB3 3.183 Fax: ++49 6159 71-2990 Planckstr. 1 mailto:h.vanhees at gsi.de D-64291 Darmstadt http://theory.gsi.de/~vanhees/index.html