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In quantum field theory, one usually encounters divergent integral when one calculates loop functions, such as the integral $\int_{0}^{\infty}dkk^{3}\frac{1}{(k^{2}-m^{2})^{2}}$ which is divergent. ...

I have a simple Fourier transform problem, originating from mathematical physics (system of linear PDEs), which reduces to taking the integral $$ I(\alpha)\equiv\int_{-\infty}^\infty e^{ikr} \cfrac{\...

We construct an $N\times N$ matrix $J$ whose elements are drawn from Gaussian distribution with zero mean and variance $\frac{1}{N}$. Since we want to have different variances for different columns, ...