# Questions tagged [regularization]

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### 1+2+3+4+… and −⅛

Is there some deeper meaning to the following derivation (or rather one-parameter family of derivations) associating the divergent series $1+2+3+4+…$ with the value $-\frac 1 8$ (as opposed to the ...
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### A proposition for summing divergent series, but how should partial summation be defined at non-natural values?

Introduction I have been in search of methods of assinging values to divergent series that have a nice intuitive or geometric interpretation. One fairly straightforward method I've considered for ...
909 views

### Divergent series summation beyond natural boundaries

I'm hoping to investigate the effects of divergent summation methods on series which cannot be analytically continued due to a dense set of singularities. At least a priori, it doesn't seem that a ...
1k views

### Value of divergent sum $\sum_{n=0}^\infty (-1)^n n^n$

I'm hoping to find a reasonable value to assign to the divergent series $\sum_{n=0}^\infty (-1)^n n^n$ and $\sum_{n=0}^\infty (-1)^n (xn)^n$. For the first one, I have obtained something around 0.71, ...
230 views

### Hypermodulus and what mathematical objects have it

When researching divergent integrals, I decided to introduce a concept of "modulus" or "determinant" of divergent integral (and series). Basically, it is the exponent of the real ...
148 views

### Improving regularity of the boundary of a convex set in Riemannian manifolds

Let $X$ be a geodesically complete Riemannian manifold (we may assume that $X$ is simply connected and negatively curved, although I don't think it matters). Given a closed, convex subset $K \subset X$...
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201 views

### Generalised limits via derivatives of integrals?

Assuming that $f$ is a continuous function, we have that $$f(x) = \frac{d}{dx}\int f(t)\,dt.$$ Assuming instead that $f$ has a removable singularity at $x=a$, and is otherwise continuous, we have ...
812 views

### Regularizing the sum of all primes

In the spirit of a similar question for the harmonic series, is there a way to regularize the (divergent) sum of all primes? $$\sum_{p \text{ prime}} p$$ Neither of these questions obtained a ...