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e_hobsbawm@hotmail.com
science forum beginner

Joined: 27 Jun 2006
Posts: 3

Posted: Wed Jul 19, 2006 1:55 pm    Post subject: Functional analysis?

My problem:

I have the function
f(r) = \int exp(-r * x) dx

I want to specify r as a linear function depending on x, so
r(x) = ax + b

Now I want in some ways to see what happens to the function "f" if I
change r(x), e.g.
f(r2) with
r2(t) = r(t) + c
or
r2(t) = r(t) + (a-c)(x-n)

What I hope to see is some form of closed form expression so I can see
how sensitive the function is for changing in some parameters.

Any tips how to start?

BR
Eric
Robert B. Israel
science forum Guru

Joined: 24 Mar 2005
Posts: 2151

Posted: Wed Jul 19, 2006 5:06 pm    Post subject: Re: Functional analysis?

<e_hobsbawm@hotmail.com> wrote:
 Quote: My problem: I have the function f(r) = \int exp(-r * x) dx

Integrating over what interval? I'll assume it's the whole real line.

 Quote: I want to specify r as a linear function depending on x, so r(x) = ax + b

If a > 0,
int_{-infty}^infty exp(-a x^2 - b x) dx = sqrt(pi/a) exp(b^2/(4 a))

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

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