Problem Statement

Provide code that produces a list of numbers which is the   nth  order forward difference, given a non-negative integer (specifying the order) and a list of numbers.

The first-order forward difference of a list of numbers   A   is a new list   B,   where   Bn = An+1 - An. List   B   should have one fewer element as a result. The second-order forward difference of   A   will be: The same as the first-order forward difference of   B. That new list will have two fewer elements than   A   and one less than   B. The goal of this task is to repeat this process up to the desired order. For a more formal description, see the related   Mathworld article.

Let's start with the solution:

proc do_fwd_diff {list} {
    set previous [lindex $list 0]
    set new [list]
    foreach current [lrange $list 1 end] {
        lappend new [expr {$current - $previous}]
        set previous $current
    }
    return $new
}

proc fwd_diff {list order} {
    while {$order >= 1} {
        set list [do_fwd_diff $list]
        incr order -1
    }
    return $list
}

set a {90.5 47 58 29 22 32 55 5 55 73.5}

for {set order 0} {$order <= 10} {incr order} {
    puts [format "%d\t%s" $order [fwd_diff $a $order]]
}