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Re: Symbolic Integration

  • To: mathgroup at
  • Subject: [mg7640] Re: [mg7635] Symbolic Integration
  • From: seanross at
  • Date: Tue, 24 Jun 1997 03:36:03 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

Die Hutte der Baba Jaga wrote:
> Hello all
> Does MMA know all the integrals known by Gradshteyn and Ryzhik?  If not,
> how come?  MMA doesn't know how to do my integral and I'd like to know
> if I should bother spending a few hours looking through G+R.  *groan*
> Is there a package that increases the number of integrals known by MMA?
> My integrals contain products of Laguerre polynomials, polynomials and
> exponents.
> much thanks!
> peter
> --
> You can sum some of the series some of the time,
> But you can't sum all of the series all of the time.
> -=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-

Funny you should ask that.  Yesterday I needed to integrate 1/(1-a
Tanh[x+x0]^2).  The mathematica result was technically true, but most
amusing in that it was the most complicated form of the expression I
could imagine.  G-R had nothing like it, so I did it by hand using
u=Tanh[x+x0], where it degenerated into a ratio of polynomials which I
let mathematica convert to simple fractions with the Apart command.  I
used this to verify the mathematica solution of the polynomial version. 
Even so, mathematica was unable to recognize the combinations of logs
that is ArcTanh in the final result.

My point:  Mathematica is not a substitute for a good working knowledge
of how to integrate or occasionally searching Gradshteyn and Rhyzik and
is certainly no substitute for pencil and paper, but it sure is a handy
tool to have around.  G-R also rarely has specialized integrals.  It
includes only basic forms, so I doubt it would have specific combination
of Laguerre polynomials.  It probably covers that in the section with
x^n Exp[-a x^m].  I am afraid you are in for some work.

A suggestion:  I have found that the mathematica Integrate routine can
occasionally be faked out by the form of an expression and especially if
it contains functions defined elsewhere in your code that you expect it
to treate symbolically.  It seems to be you need to do some algebra
first, since any combination of x^n Exp[a x^m] can be solved.  If you
reduce your integrand to combinations of these terms, you should be able
to let mathematica do the integration.  Good Luck.

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