Robuta

Sponsor of the Day: Jerkmate
https://matkafasi.com/141805/lim-limits-x-to-infty-left-frac-1-sin-2x-frac-1-x-2-right $$\lim\limits_{x\to \infty}\left(\frac{1}{\sin^2x}-\frac{1}{x^2}\right)=?$$ - Matematik Kafası $$\lim\limits_{x\to \infty}\left(\frac{1}{\sin^2x}-\frac{1}{x^2}\right)=?$$ 1 sin2x 2liminftyleft https://mathoverflow.net/questions/366484/how-to-prove-that-sum-m-0-infty-gamma-12m-alpha-over-gamma1 pr.probability - How to prove that $ \sum_{m=0}^{\infty} { \Gamma\{(1+2m)/\alpha\}\over... I would love to prove the following inequality $$ {1\over \sqrt{\pi} } \sum_{m=0}^{\infty} \Gamma\{(1+2m)/\alpha\} { (-t^2)^{m}\over (2m) !}=$$ $$... pr probability0 infty1 2mprovesum https://mathoverflow.net/posts/366302/timeline Timeline for Prove $\int_{0}^{\infty} \cos(\omega x) \exp(-x^{\alpha}) \, {\rm d} x \ge {\alpha^2... int 0omega xge 2timelineprove https://mathoverflow.net/questions/509633/is-the-xin-prod-k-1-infty-textlcm1-2-dots-lfloor-n1-k-r nt.number theory - Is the $\Xi(n) = \prod_{k=1}^{\infty} \text{lcm}(1, 2, \dots, \lfloor n^{1/k}... In this previous discussion, it was demonstrated that the standard Least Common Multiple sequence $\text{lcm}(1, 2, \dots, n)$ is not a subset of the highly... nt number theoryk 1xiprod https://mathoverflow.net/questions/366302/prove-int-0-infty-cos-omega-x-exp-x-alpha-rm-d-x-ge-alp pr.probability - Prove $\int_{0}^{\infty} \cos(\omega x) \exp(-x^{\alpha}) \, {\rm d} x \ge... I would like to prove that $$\int_{0}^{\infty} \cos(\omega x) \exp(-x^{\alpha}) \, {\rm d} x \ge {\alpha^2 \sqrt{\pi} \over 8} \exp \left( -\frac{\omega^2}{4}... pr probabilityint 0omega xproveinfty