PHP mktime隐藏了可读格式

How do I make a new variable that takes the value from mktime value below. I tried the following and it did not work.

$new_date = $display_day->format('l, F d');

Here is the original script

if (array_key_exists('day', $_GET)) {
    $add_day = $_GET['day'];
} else {
    $add_day = 0;
}

$display_day = mktime(0, 0, 0, date("m")  , date("d") + $add_day, date("Y"));


$today = date('N', $display_day);

This is easier using DateTime()

$display_day = new DateTime();
$display_day->modify("+ $add_day days");
$new_date = $display_day->format('l, F d');