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Re: RE: RE: ExpIntegralEi

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  • Subject: [mg18684] Re: [mg18632] RE: [mg18491] RE: [mg18463] ExpIntegralEi
  • From: "Kevin J. McCann" <kevinmccann at>
  • Date: Thu, 15 Jul 1999 01:46:02 -0400
  • References: <>
  • Sender: owner-wri-mathgroup at


You have hit it exactly. Since the real and imaginary parts of the original
integrand ARE well-defined, well-behaved, etc. There is NO mathematical
ambiguity and certainly no computational ambiguity. I believe that Hendrik's
assertion that both answers are equally valid is incorrect.  This is easily
seen from the definition of a Riemann integral of well-defined, etc.
function.  Conclusion - the numerical integration is correct (to the
accuracy of the numerics), the symbolic answer to the DEFINITE integral is

My two cents worth,


----- Original Message -----
From: Andrzej Kozlowski <andrzej at>
To: mathgroup at
<arnaud at>; <m.van.almsick at>;
<kevinmccann at>; <h.vanhees at>
Subject: [mg18684] Re: [mg18632] RE: [mg18491] RE: [mg18463] ExpIntegralEi
> An integral like the one considered here is simply an integral of a
> valued function over a measurable subset of R^2.  This is just a special
> case of a more general concept of an integral of a function with values in
> Banach space (called a Bochner integral) and evaluating it simply amounts
> evaluating its real and imaginary parts separately and taking the
> complex number. All that is required for such an integral to be well
> is that the real and imaginary parts of the function  be integrable real
> functions. Such an integral can always quite unambiguously  be evaluated
> simply by evaluating its real and imaginary parts separately. Each of
> can be reduced two repeated computation of ordinary integrals by Fubini's
> theorem:


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