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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) + (ac)(xn)
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 

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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?



In article <1153317334.024628.244660@p79g2000cwp.googlegroups.com>,
<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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