Questions tagged [integration]

Concerns all aspects of integration, including the integral definition and computational methods. For questions solely about the properties of integrals, use in conjunction with (indefinite-integral), (definite-integral), (improper-integrals) or another tag(s) that typically describe(s) the types of the integrals being considered. This tag often goes along with the (calculus) tag.

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7
votes
1answer
191 views
+100

Representing the determinant of a Hermitian matrix as an integral

Let $M=\left (\omega\mathbb{I}-A\right )\left(\omega^{*}\mathbb{I}-A^{\dagger}\right)$ be a Hermitian matrix of size $n\times n$ where $A$ is a real non symmetric matrix and $\omega=a+\mathrm{i}b$. $A^...
10
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1answer
302 views
+100

Challenging integral: Evaluate $\int_0^1\frac{\ln^3(1-x)\operatorname{Li}_3(x)}{x}\ dx$

How to evaluate $$I=\int_0^1\frac{\ln^3(1-x)\operatorname{Li}_3(x)}{x}\ dx\ ?$$ I came across this integral $I$ while I was trying to compute two advanced sums of weight 7. The problem with my ...
0
votes
0answers
64 views
+50

Integral over Markov Process

I have two integrals $$\int_{0}^{\infty} \mathbb{E}[\cos 2 \psi(0) \cos 2 \psi(z)] d z$$ $$\int_{0}^{\infty} \mathbb{E}[\sin 2 \psi(0) \sin 2 \psi(z)] d z$$ where $\psi(z)$ is randomly varying ...