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Re: Problem with Integrate

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  • Subject: [mg25996] Re: Problem with Integrate
  • From: Hendrik van Hees <h.vanhees at>
  • Date: Wed, 15 Nov 2000 02:09:46 -0500 (EST)
  • References: <8ur14j$>
  • Sender: owner-wri-mathgroup at

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

(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
D-64291 Darmstadt

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