irregular summations in Home/CAS

[Albert Chan]

(10-26-2024 01:28 PM)Wes Loewer Wrote:  I thought the whole point of this definition was that this works with any values, even negatives.
Please give an example in which this would not be true.

sum with negative elements is undefined.
OP already give an example, Σ(K^2,K,5,1), element counts = 1 - 5 + 1 = -3

If we say negative count is forbidden, we get ERROR
If we say elements based from 5 ≤ K ≤ 1, we get 0

If we are allowed to flip the limits a certain way, so that element count is positive, we get this

Σ(K^2,K,5,1) = -Σ(K^2,K,2,4) = -(2^2 + 3^2 + 4^2) = -29

We are not saying sum is correct.
We simply ASSIGN a [logically consistent] value for the sum.

Example, zeta(-1) = 1 + 2 + 3 + ... = -1/12