Recent content by Ssnow

I solved the problem, Ssnow

Interesting videos, for me the hyperdie is more intuitive than the hypersphere ... Ssnow

Hi to all!! I have a problem to derive the conformal laplacian \sum_{m,n}g^{mn}(y)\partial_{q^m}\partial_{q^n}(\psi|\det{(g)}|^{1/4})(y)=\sum_{m,n}|det{g}|^{1/4}(\Delta \Psi -\frac{1}{6}R(y)\psi(y)) where $$g$$ is the metric associated to a Levi Civita connection in a normal frame, we have...

Hi, I think there is an error in the last term, this must be zero because you must be able to reconstruct the conservation condition ... Ssnow

Hi, if you use the TikZ library there is a command \moon{<day>} that takes the day of the lunar month as an argument and draws the corresponding lunar phase ... Ssnow

I think you can try to have a infinite sum expanding by Taylor the exponential: ## \int e^{\cos(x)}dx=\int 1+\cos{x}+\frac{\cos^2{x}}{2!}+\frac{\cos^3{x}}{3!} dx ## now by linearity: ## \int e^{\cos(x)}dx=x+\sin{x}+\int\frac{\cos^2{x}}{2!} dx+\int \frac{\cos^3{x}}{3!} dx + ...## If you have...

I think the notation of @pasmith is appropriate, thank you! Ssnow

Hi Physics Forum, I want to ask if there is an "appropriate" notation for the infinite self-iteraction of an analytic function ##f(x)##, that is ##f(f(f(...)))##. For example I know ##f^{(+\infty)}(x)## can be a way, but there is an operator notation as for the infinite sum...

"Quantum computation and quantum Information" by Nielsen e Chuang. Ssnow

Hi, yes I think the substitution can be of the following form ## \alpha \,=\, \frac{50}{\pi}t## do the differential will be ##d\alpha\,=\,\frac{50}{\pi}dt## and inverting ##dt\,=\, \frac{\pi}{50} d\alpha##, now put it into your integral ... 😄 Ssnow

Hi, there is a relation between degrees and time if you have the frequency ... because ##f=2\pi \omega## where ##\omega## is the angular velocity (or pulsation). If you write ##\omega=\frac{\Delta \alpha}{\Delta t}## you have that ## \Delta \alpha = \frac{f}{2\pi}\Delta t##, or simply...

You can start rewriting the function ##f(x)=(1-cx)^{\frac{1}{x}}## as ##f(x)=e^{\frac{\log{(1-cx)}}{x}}## that is equivalent to your function because exponential is the inverse of logarithm (and using a property of log). Now you can calculate the Taylor expansion by the formula: ## f(x)=...

In Mathematical Logic ##dx## denotes an infinitesimal number. An infinitesimal number is an hyper-real number that is not contained in the set ##\mathbb{R}##. We can define the infinitesimal number ##dx## by the relation ## dx < \frac{1}{n} ## for each ##n\in \mathbb{N}##. We can call this...

I think that the question is "very thin" the two equations: ## 2x\Delta x +\Delta x^2## for ##\Delta x \rightarrow 0## and ##x+x^2## for ##x\rightarrow 0## are conceptually different because are two different objects. The first equation approximated to the first order gives ##2xdx##, the second...

This is another form for the product integral ...