Re: How to solve this type of equation in Mathematica?
- To: mathgroup at smc.vnet.net
- Subject: [mg59976] Re: How to solve this type of equation in Mathematica?
- From: robert.dodier at gmail.com
- Date: Sat, 27 Aug 2005 04:11:05 -0400 (EDT)
- References: <dehk3h$c9t$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
> That is I would like to solve for f(x) when we know that
> integrating (x + P) f(x) from P to Infinity over x equals 1.
It looks to me like this isn't strong enough
to yield a unique solution (or even a solution in
a well-known class).
If you replace f by A f where A is a constant
you get A times \int_P^{\infty} (x + P) f(x) dx.
So let f be any function s.t. the integral is defined
and not equal to zero. (I believe that's a fairly
large class.) If the integral I is not equal to 1,
replace f by f/I and that's a solution,
if I'm not mistaken.
The equation is an example of an integral equation,
so you might be able to find more info under that
heading. Sorry that I can't be more helpful.
Robert Dodier