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Wen...
Posted: Tue Jun 02, 2009 11:31 pm
 
Hi all,

Does the integral (either definite or indefinite) of exp(1/x) have a
close form solution? Or is it a must to solve such an integral using
numerical methods? If so, can you recommend some good (or
conventional) numerical methods to calculate that? Thanks a lot in
advance.
 
Martin Musatov...
Posted: Tue Jun 02, 2009 11:39 pm
 
Martin Musatov wrote:

Wen wrote:
[quote:a4b3e94c38]Hi all,

Does the integral (either definite or indefinite) of exp(1/x) have a
close form solution? Or is it a must to solve such an integral using
numerical methods? If so, can you recommend some good (or
conventional) numerical methods to calculate that? Thanks a lot in
advance.
P=NP=Definite.(1)[/quote:a4b3e94c38]
~Musatov
 
Andrew Tomazos...
Posted: Wed Jun 03, 2009 12:25 am
 
On Jun 3, 11:31 am, Wen <huangwe... at (no spam) gmail.com> wrote:
[quote:1c2a117d71]Hi all,

Does the integral (either definite or indefinite) of exp(1/x) have a
close form solution? Or is it a must to solve such an integral using
numerical methods? If so, can you recommend some good (or
conventional) numerical methods to calculate that? Thanks a lot in
advance.
[/quote:1c2a117d71]
The integral of e^(1/x) is

x(e^(1/x)) - Ei(1/x)

where Ei is the exponential integral function...

http://en.wikipedia.org/wiki/Exponential_integral

Enjoy,
Andrew.
 
Wen...
Posted: Wed Jun 03, 2009 12:33 am
 
On Jun 3, 6:25 pm, Andrew Tomazos <and... at (no spam) tomazos.com> wrote:
[quote:51479ebffd]On Jun 3, 11:31 am, Wen <huangwe... at (no spam) gmail.com> wrote:

Hi all,

Does the integral (either definite or indefinite) of exp(1/x) have a
close form solution? Or is it a must to solve such an integral using
numerical methods? If so, can you recommend some good (or
conventional) numerical methods to calculate that? Thanks a lot in
advance.

The integral of e^(1/x) is

    x(e^(1/x)) - Ei(1/x)

where Ei is the exponential integral function...

   http://en.wikipedia.org/wiki/Exponential_integral

Enjoy,
Andrew.
[/quote:51479ebffd]
Thanks for the solution. And it turns out that exp(1/x) is only a part
of the the function to be integrated. So I am going to use numerical
methods finally. So can you recommend some numerical methods to do
that? Thanks.
 
Wen...
Posted: Wed Jun 03, 2009 12:34 am
 
On Jun 3, 5:39 pm, Martin Musatov <marty.musa... at (no spam) gmail.com> wrote:
[quote:5de11dcc9b]Martin Musatov wrote:
Wen wrote:
Hi all,

Does the integral (either definite or indefinite) of exp(1/x) have a
close form solution? Or is it a must to solve such an integral using
numerical methods? If so, can you recommend some good (or
conventional) numerical methods to calculate that? Thanks a lot in
advance.

P=NP=Definite.(1)
~Musatov
[/quote:5de11dcc9b]
What do you mean?
 
Han de Bruijn...
Posted: Wed Jun 03, 2009 5:00 am
 
Wen wrote:

[quote:02b9a59ce9]On Jun 3, 5:39 pm, Martin Musatov <marty.musa... at (no spam) gmail.com> wrote:

Martin Musatov wrote:
Wen wrote:

Hi all,

Does the integral (either definite or indefinite) of exp(1/x) have a
close form solution? Or is it a must to solve such an integral using
numerical methods? If so, can you recommend some good (or
conventional) numerical methods to calculate that? Thanks a lot in
advance.

P=NP=Definite.(1)
~Musatov

What do you mean?
[/quote:02b9a59ce9]
Nothing. You'd better just ignore Musatov. He is appending his nonsense
at virtually every posting he can find in 'sci.math'.

Han de Bruijn
 
Fatal...
Posted: Wed Jun 03, 2009 6:25 am
 
Wen a écrit :
[quote:ceae260d6f]Hi all,

Does the integral (either definite or indefinite) of exp(1/x) have a
close form solution? Or is it a must to solve such an integral using
numerical methods? If so, can you recommend some good (or
conventional) numerical methods to calculate that? Thanks a lot in
advance.
[/quote:ceae260d6f]
The theory of differential fields gives a sense to "closed form of an
antiderivative" and Liouville's theorem deals with this existence.

Here is a corollary of this theorem: consider a function f*exp(g) where
f and g are quotients of polynomials, g non constant. If this function
has an elementary antiderivative (that is, obtained within a finite
number of steps from the field of rational fractions taking algebraic
extensions, eps and logs) then this antiderivative has the form
h*exp(g), h a rational fraction.

--
Fatal
 
alainverghote at (no spam) gmail.com...
Posted: Wed Jun 03, 2009 10:10 pm
 
On 3 juin, 14:25, Fatal <fa... at (no spam) yahoo.fr> wrote:
[quote:44d6088b4f]Wen a écrit :

Hi all,

Does the integral (either definite or indefinite) of exp(1/x) have a
close form solution? Or is it a must to solve such an integral using
numerical methods? If so, can you recommend some good (or
conventional) numerical methods to calculate that? Thanks a lot in
advance.

The theory of differential fields gives a sense to "closed form of an
antiderivative" and Liouville's theorem deals with this existence.

Here is a corollary of this theorem: consider a function f*exp(g) where
f and g are quotients of polynomials, g non constant. If this function
has an elementary antiderivative (that is, obtained within a finite
number of steps from the field of rational fractions taking algebraic
extensions, eps and logs) then this antiderivative has the form
h*exp(g), h a rational fraction.

--
Fatal
[/quote:44d6088b4f]
Dear Wen,

For the definite integral of exp(1/x) you'll find simple numerical
proxies.
Example for large values of the lower limit we may adjust to a
fraction p(n)(x)/q(n)(x) , p and q two n polys,
For very large values exp(1/x) ~(2x+1)/(2x-1) will do,

Alain
 
Bill...
Posted: Thu Jun 04, 2009 2:30 pm
 
<alainverghote at (no spam) gmail.com> wrote in message
news:4f0cf3fd-7fb6-4117-ba36-fc37c94741c7 at (no spam) o14g2000vbo.googlegroups.com...
On 3 juin, 14:25, Fatal <fa... at (no spam) yahoo.fr> wrote:
[quote:019ecf057a]Wen a écrit :

Hi all,

Does the integral (either definite or indefinite) of exp(1/x) have a
close form solution? Or is it a must to solve such an integral using
numerical methods? If so, can you recommend some good (or
conventional) numerical methods to calculate that? Thanks a lot in
advance.

The theory of differential fields gives a sense to "closed form of an
antiderivative" and Liouville's theorem deals with this existence.

Here is a corollary of this theorem: consider a function f*exp(g) where
f and g are quotients of polynomials, g non constant. If this function
has an elementary antiderivative (that is, obtained within a finite
number of steps from the field of rational fractions taking algebraic
extensions, eps and logs) then this antiderivative has the form
h*exp(g), h a rational fraction.

--
Fatal
[/quote:019ecf057a]
Dear Wen,

For the definite integral of exp(1/x) you'll find simple numerical
proxies.
Example for large values of the lower limit we may adjust to a
fraction p(n)(x)/q(n)(x) , p and q two n polys,
For very large values exp(1/x) ~(2x+1)/(2x-1) will do,

Alain

In the above sense, wouldn't the asymptote y=y(x) =1 do just as well?
 
alainverghote at (no spam) gmail.com...
Posted: Thu Jun 04, 2009 8:52 pm
 
On 4 juin, 22:30, "Bill" <Bill_NOS... at (no spam) comcast.net> wrote:
[quote:d5e39bb9b8]alainvergh... at (no spam) gmail.com> wrote in message

news:4f0cf3fd-7fb6-4117-ba36-fc37c94741c7 at (no spam) o14g2000vbo.googlegroups.com...
On 3 juin, 14:25, Fatal <fa... at (no spam) yahoo.fr> wrote:





Wen a écrit :

Hi all,

Does the integral (either definite or indefinite) of exp(1/x) have a
close form solution? Or is it a must to solve such an integral using
numerical methods? If so, can you recommend some good (or
conventional) numerical methods to calculate that? Thanks a lot in
advance.

The theory of differential fields gives a sense to "closed form of an
antiderivative" and Liouville's theorem deals with this existence.

Here is a corollary of this theorem: consider a function f*exp(g) where
f and g are quotients of polynomials, g non constant. If this function
has an elementary antiderivative (that is, obtained within a finite
number of steps from the field of rational fractions taking algebraic
extensions, eps and logs) then this antiderivative has the form
h*exp(g), h a rational fraction.

--
Fatal

Dear Wen,

For the definite  integral of exp(1/x) you'll find simple numerical
proxies.
Example for large values of the lower limit we may adjust to a
fraction p(n)(x)/q(n)(x)  , p and q two n polys,
For very large values exp(1/x) ~(2x+1)/(2x-1) will do,

Alain

In the above sense, wouldn't the asymptote y=y(x) =1 do just as well?- Masquer le texte des messages précédents -

- Afficher le texte des messages précédents -
[/quote:d5e39bb9b8]
Bonjour,

Depends upon the size of the lower limit!

Alain
 
 
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