1
$\begingroup$

I'm trying to evaluate or simplify this integral:

$$I_{a,b,c} = \int_{a}^{+\infty} \frac{\exp(-bx)}{x+c} Ei(x) dx $$

with $a,b,c \in \mathbb{R}_+^*$. and $ Ei(x) =\int_{-\infty}^{x} \frac{\exp(t)}{t} \mathbb{d}t $ : The Exponential integral function

Any ideas, hints, directions would be highly appreciated.

$\endgroup$
3
  • $\begingroup$ Why? ${}{}{}{}$ $\endgroup$
    – Will Jagy
    Jun 2, 2012 at 2:35
  • 1
    $\begingroup$ Feeding this integral into Mathematica returns it unevaluated. This means that it is unlikely that this integral can be exactly evaluated even in terms of such a general class of special functions as Meijer G functions. In other words, it is unlikely that the answer is in any kind of recognizable "closed form". In that case, any "simplification" that can be done to this integral depends very strongly on what you intend to do with it. Possibilities: asymptotic expansion in a parameters, satisfying a differential equation in parameters, suitability for numeric integration. Please clarify. $\endgroup$ Jun 2, 2012 at 23:43
  • $\begingroup$ Maple 15 can't even do simple cases like $a=0,b=c=1$ and $a=b=1,x=0$. $\endgroup$ Jun 3, 2012 at 7:32

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.