06/06/2011, 11:01 AM

ive noticed we used both the terms vandermonde and carleman matrix.

ofcourse its carleman matrix and not vandermonde !

also note that the 2 matrix-method number must sum to 1 !!

0.580243966210

+

0.41975603379

=0.9999999999 = 1

simply because 1/(1+x) + 1/(1+(1/x)) = 1.

- which also shows the importance of the determinant !! -

because of this sum = 1 , the matrix methods cannot match the serial summation.(*)

this is similar to my determinant argument made before , just an equivalent restatement.

* the sum of both serials is related to the equation f(g(x)) = f(x) , whereas the sum of matrix methods just gives 1 for all x.

ofcourse its carleman matrix and not vandermonde !

also note that the 2 matrix-method number must sum to 1 !!

0.580243966210

+

0.41975603379

=0.9999999999 = 1

simply because 1/(1+x) + 1/(1+(1/x)) = 1.

- which also shows the importance of the determinant !! -

because of this sum = 1 , the matrix methods cannot match the serial summation.(*)

this is similar to my determinant argument made before , just an equivalent restatement.

* the sum of both serials is related to the equation f(g(x)) = f(x) , whereas the sum of matrix methods just gives 1 for all x.