Question: why such error but simply result still stayed as a heritage in 12.02..!!!

_f:=(k,n,X)->f[k]*product(X-x[_i],_i=0..k-1)*product(X-x[_i],_i=k+1..n)/
> (product(x[k]-x[_i],_i=0..k-1)*product(x[k]-x[_i],_i=k+1..n));
  _f := (k, n, X) ->

             /  k - 1               \ /    n                 \
             | --------'            | | --------'            |
             |'  |  |               | |'  |  |               |
        f[k] |   |  |    (X - x[_i])| |   |  |    (X - x[_i])|
             |   |  |               | |   |  |               |
             |   |  |               | |   |  |               |
             \  _i = 0              / \_i = k + 1            /
        -------------------------------------------------------
        /  k - 1                  \ /    n                    \
        | --------'               | | --------'               |
        |'  |  |                  | |'  |  |                  |
        |   |  |    (x[k] - x[_i])| |   |  |    (x[k] - x[_i])|
        |   |  |                  | |   |  |                  |
        |   |  |                  | |   |  |                  |
        \  _i = 0                 / \_i = k + 1               /

>
> F:=(y,n)->Sum(_f(j,n,y),j=(0..n));

                                   _N
                                  -----
                                   \
                  F := (y, _N) ->   )   _f(j, _N, y)
                                   /
                                  -----
                                  j = 0
Here :
> F(x[3],3);
>

                                 3
                               -----
                                \
                                 )   0
                                /
                               -----
                               j = 0
But ,
> _f(0,3,x[3])+_f(1,3,x[3])+_f(2,3,x[3])+_f(3,3,x[3]);

                                 f[3]

> F(x[3],4);

    4        /  j - 1                  \ /    4                    \
  -----      | --------'               | | --------'               |
   \         |'  |  |                  | |'  |  |                  |
    )   f[j] |   |  |    (x[3] - x[_i])| |   |  |    (x[3] - x[_i])|
   /         |   |  |                  | |   |  |                  |
  -----      |   |  |                  | |   |  |                  |
  j = 0      \  _i = 0                 / \_i = j + 1               /

             //  j - 1                  \ /    4                    \
             || --------'               | | --------'               |
           / ||'  |  |                  | |'  |  |                  |
          /  ||   |  |    (x[j] - x[_i])| |   |  |    (x[j] - x[_i])|
         /   ||   |  |                  | |   |  |                  |
             ||   |  |                  | |   |  |                  |
             \\  _i = 0                 / \_i = j + 1               /

        \
        |
        |
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        |
        |
        /