09/23/2013, 08:50 PM
The only contour summation I believe in is the riemann sum of a contour integral.
A few reasons
1) If the sum is over finite terms , the value DOES depend on the path.
2) If the sum is over infinite terms , the set MUST be dense on the path ( such as gaussian rational approximations ).
3) If the sum is over a non fixed amount of terms , it is continuum summation. Or conditional continuum summation.
4) the arguments above apply to all types of numbers and dimensions ( real complex bicomplex etc )
I tried to counter my own arguments for about a week but failed, hence Im confident that contour summation does not exist ?
I once considered uncountable sums , but they turned out to be equivalent to contour integration too.
So I doubt the consistancy of the idea of contour summation.
regards
tommy1729
A few reasons
1) If the sum is over finite terms , the value DOES depend on the path.
2) If the sum is over infinite terms , the set MUST be dense on the path ( such as gaussian rational approximations ).
3) If the sum is over a non fixed amount of terms , it is continuum summation. Or conditional continuum summation.
4) the arguments above apply to all types of numbers and dimensions ( real complex bicomplex etc )
I tried to counter my own arguments for about a week but failed, hence Im confident that contour summation does not exist ?
I once considered uncountable sums , but they turned out to be equivalent to contour integration too.
So I doubt the consistancy of the idea of contour summation.
regards
tommy1729