Need help to create a function which is equivalent to an other function.

You've only defined the product loop - I can't see where you've defined the summation equivalent?

In your definition of N1 the product runs from 0 to k-1 and is inside the summation with index k starting at 0. That way you would address vector element -1 which does not exist (assuming ORIGIN=0). This is to be avoided as summation and product react somewhat illogical in that situation.

Does N1 give you the desired result? Even then you should rewrite it.

You can easily rewrite your function N1 withou using sum and product using three nested for-loops for n, k and j, while I can see no reason why you should want to do so! The new function will produce different results because auf that failure above (you will get expressions with (a[-1.