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You could then create a file called foo.rss or whatever and configure your server via htaccess to handle the file as .php then use a php include to include the search results page search.php?query=whatever
This is assuming you use php. Any other scripting language should be able to do the same.
What you would be looking for is something like
<url>the result url</url>
for each individual result. You should be able to do this by editing your search scripts template file or the actual code within your search script file.
Then create a script to call the result page. Call it something like queryfeed.php
<?xml version="1.0" encoding="iso-8859-1"?>
How what you will have is a php page that outputs rss when a query is sent within the url. For example example.com/queryfeed?q=test
You now need to set up apache to handle this file. Rename queryfeed.php to queryfeed.rss
Because it is no longer an php file it will no longer work. what you need to do is add an entry to your htaccess to allow the rss file to be handles in the same way as php.
create a .htaccess file in the directory that holds your queryfeed.rss file and place the following code within in.
Hope this helps.