Re: Here Is What I Believe is the Solution

On Nov 28, 6:27 pm, "Jay R. Yablon" <jyab...@xxxxxxxxxxxx> wrote:
"Dono" <sa...@xxxxxxxxxxx> wrote in message

news:4fc7beaa-0c47-44f7-904f-4aa035eab33f@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

On Nov 28, 8:33 am, Albertito <albertito1...@xxxxxxxxx> wrote:
On Nov 28, 3:30 pm, Eric Gisse <jowr...@xxxxxxxxx> wrote:

On Nov 27, 7:31 pm, "Jay R. Yablon" <jyab...@xxxxxxxxxxxx> wrote:

As to the problem I posted yesterday, I have received several
opinions
across several Usenet groups (including here) that there is no
closed
form for the integral $ from -oo to +oo which I will represent
here as:

$dx exp[-Ax^4-Bx^3-.5Kx^2+Jx]

I believe there is a closed form, and that one can do this to any
order
and is not limited to only fourth order. Please tell me if you
agree.

Solution (maybe?) posted below.

http://jayryablon.files.wordpress.com/2008/11/polynomial-solution-wri...

Thanks,

Jay.

Comments on my attempt would be appreciated, especially since it
took
a fair while to find a method that worked.

Ok, I'll comment your attempt: Your attempt is plain bull***!
It's funny to see a "genius" of mathematics like Eric inventing
integration methods :-) Seriously, how old are you, kid?

Your initial integral

I = int( exp( Jx - 1/2 [Ax + gx^2]^2 ), x = -\infty...\infty)

comes after a variable substitution that is badly incorrect,
namely x->x(A + gx). As I've pointed out, for sake of clarity,
call the new variable 'u', such that the substitution is

x = u(A + gu),

<rest of imbecilities snipped>

AlbertShito Imbecile,

The substitution x = u(A + gu) makes the problem even WORSE. Do you
know why, cretin?

What Jay was talking about is using the substitution:

x(A+gx)=u

He eventually abandoned this idea in favor of another approach (that
is obviously to advanced for your cretinoid brain).

Oh, my virgin ears, with all this foul language and silly bickering! ;-)

Anyway,

Dono is correct that I was using the substitution x(A+gx)=u and
eventually abandoned that idea.

I used this at the start because it retained the form of an $dx
e^(-.5x^2) even with terms in fourth order of x.

That is in part because I thought that one could not obtain a closed
solution except for certain special cases that could be converted over
to the $dx.e^(-.5x^2) form.

I abandoned this a) because the way I handled the substitution was wrong
as people in several Usenet groups pointed out and b) because I realized
that one could obtain a closed form solution for

$dx e^V(x)

where V(x) is a *any* polynomial of *any* order so long as V(x) includes
first and second order terms. Clearly, that is preferable to the very
restricted case I started with on the false assumption that only special
restricted cases would admit closed solutions.

Jay.

No, Dono is not correct, he never was correct and never
will. He is the person that always starts insulting people.
With regards to your problem, I have to admit that the
substitution x(A+gx)=u is nonsense if x is the old variable
and u the new one, because that is not what was reflected in
your subsequent steps, ...

.