output specific location in the header

Okay, here is a working example of what you (might) want to do.

Put the following in your functions.php:

add_action('wp_head', 'my_jquery_code', 999999999);
function my_jquery_code() {
    $jquery_code = <<<JQUERY
<script>
    // jQuery code goes here...
</script>
JQUERY;
    echo $jquery_code.PHP_EOL;
} // function my_jquery_code