### Questions (69)

 22 Is there a way to deal with this singularity in numerical integration? 16 Is there a way to evaluate analytically the following infinite double sum? 12 Why solving a differentiated integral equation might eventually lead to erroneous solutions of the original problem? 8 Behavior of a function defined by two infinite integrals around the singularity point 7 How to solve a second order partial differential equation involving a delta Dirac function?

### Reputation (700)

 +20 Factorizing $f(\lambda, R) = -6+4\lambda+6R-2R^2+2\lambda R^2-5\lambda R$ for $(\lambda, R)\in \mathbb{R}^2$ +10 What is $\left( \boldsymbol{e} \, \cdot \, \boldsymbol{\nabla} \right) \left( \boldsymbol{a} \times \boldsymbol{b} \right)$ +10 When this $f(x)=\frac{\log x}{x}$ decreasing and when is it increasing +10 Why swapping between the derivative operator and this infinite sum leads to different results?

 6 Evaluating a Lebesgue Integral 4 Given, $x=\cos \theta +i \sin \theta$, then find $x-x^{-1}$? 2 $\lim_{x\to ∞} \sqrt{x+\sin(x)/{(x-\cos^2(x))}}$ 2 Prove the Chapman-Kolmogorov equation for Brownian motion 1 When this $f(x)=\frac{\log x}{x}$ decreasing and when is it increasing

### Tags (79)

 8 integration × 48 4 trigonometry × 7 6 real-analysis × 36 3 calculus × 14 6 definite-integrals × 23 2 indefinite-integrals × 13 6 algebra-precalculus × 2 2 limits × 4 6 lebesgue-integral 2 stochastic-analysis