This function had been marked as deprecated.

This was once used to kick-off the Core Updater.

Deprecated in favor of instantating a Core_Upgrader instance directly, and calling the ‘upgrade’ method.

Signature

wp_update_core( $current, $feedback = '' )
current
 
feedback
 
Default: ''

Return

(void)

Source

function wp_update_core($current, $feedback = '') {
	_deprecated_function( __FUNCTION__, '3.7', 'new Core_Upgrader();' );

	if ( !empty($feedback) )
		add_filter('update_feedback', $feedback);

	include ABSPATH . 'wp-admin/includes/class-wp-upgrader.php';
	$upgrader = new Core_Upgrader();
	return $upgrader->upgrade($current);

}
WP Trac GitHub

Link here