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Questions tagged [divergent-integrals]

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Integral involving a Gaussian and a fraction.

This question is a generalization of An identity involving the incomplete Beta function. . Let $x\ge 0$ and $\epsilon_\pm \in (1,\infty)$. We consider the following integral: \begin{equation} {\...
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Why does the divergence in my integral has a change of type?

I am looking at the following integral in Euclidean space: $$I = \int_{\mathbb{R}} d\tau_3 \int_{\mathbb{R}} d\tau_4 \int_{\mathbb{R}^4} d^4 x_5 \frac{1}{x_{15}^2 x_{25}^2 x_{35}^2 x_{45}^2} \tag{1}$$...
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Is this integral always valid?

The following integral was integrated using Mathematica: $$\int_{-\infty}^{\infty} d\tau \frac{1}{(x^2+\tau^2)^a} = \frac{\Gamma(a-1/2)}{\Gamma(a)}\frac{\sqrt{\pi}}{|x|^{2 a -1}} \tag{1}$$ ...
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What are the algebraic properties of this numerical system?

The system is introduced here: https://mathoverflow.net/questions/115743/an-algebra-of-integrals/342651#342651 Particularly, there are some elements by which we cannot divide. Does it tell something ...
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For two divergent integrals, is it possible to meaningfully construct a divegent integral that would be in a sense their product?

I want to see a rule that would transform two integrals $\int_0^\infty f(x)dx$ and $\int_0^\infty g(x)dx$ into $\int_0^\infty h(x)dx$ in such a way that it would have properties of a product. First, ...