Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1994
*January
*February
*March
*April
*May
*June
*July
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1994

[Date Index] [Thread Index] [Author Index]

Search the Archive

triple integral

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: triple integral
  • From: dario at rs3.csrsrc.mi.cnr.it (Dario Bressanini)
  • Date: Tue, 15 Mar 1994 12:09:40 +0100

I am having problem with a triple integral.


<<Local`Declare`
Declare[{s,t,g1,g2},Positive]

q = Exp[-g1 s -g2 t]/u

a1 = Integrate[q,{s,0,Infinity},{u,0,s},{t,-u,u}]
Integrate::gener: Unable to check convergence.
                                                                   g2       3
Series::esss:Essential singularity encountered in ExpIntegralEi[-(--) + O[s]].
                                                                   s
                                                                   g2        3
Series::esss:Essential singularity encountered in ExpIntegralEi[-(--) + O[s]].
                                                                   s
                                                                 -g1 - g2    3
Series::esss:Essential singularity encountered in ExpIntegralEi[-------- +O[s]].
                                                                    s

General::stop: Further output of Series::esss will be suppressed during this calculation.

         g1            g1
-Log[1 - --] + Log[1 + --]
         g2            g2
--------------------------
          g1 g2


This is the answer, as a function of g1 and g2. The problem is that 
if g2<g1 we get a complex answer, which is wrong

a1 /. {g1->2,g2->1}

-I Pi + Log[3]
--------------
      2

N[%]

0.549306 - 1.5708 I

If i try to substitute directly g1 and g2 in the integral, I get a funny
result:

q1 = q /. {g1->2,g2->1}

a2 = Integrate[q1,{s,0,Infinity},{u,0,s},{t,-u,u}]
Integrate::gener: Unable to check convergence.
                                                                 -3       3
Series::esss: Essential singularity encountered in ExpIntegralEi[-- + O[s] ].
                                                                 s
                                                                 -3       3
Series::esss: Essential singularity encountered in ExpIntegralEi[-- + O[s] ].
                                                                 s
                                                                 -3       3
Series::esss: Essential singularity encountered in ExpIntegralEi[-- + O[s] ].
                                                                 s
General::stop: Further output of Series::esss will be suppressed during this calculation.
          -ExpIntegralEi[-s] + ExpIntegralEi[s]
Integrate[-------------------------------------, {s, 0, Infinity}]
                           2 s
                          E

It seems that MMA is not able now to evaluate the integral that was
able to evaluate before. But this is not the problem, since by doing
one integration at a time we get the previous WRONG result,
Infact, if we use NIntegrate[]:

a3 = NIntegrate[q1,{s,0,Infinity},{u,0,s},{t,-u,u}]

0.549306

How can i correct this behaviour? (I mean, I know that if I do
something like  Log[a_] -> Log[Abs[a]] I get only real number,
but this is not a solution, since i have many integrals of this type
to compute and this hack may not work or may be wrong)

Any help?       dario Bressanini     dario at rs3.csrsrc.mi.cnr.it





  • Prev by Date: Re: Stupid Mma Tricks
  • Next by Date: Real Roots of cubics
  • Previous by thread: Integral of unbounded function.
  • Next by thread: Real Roots of cubics