Recent content by 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 ...

You can see this article: https://arxiv.org/pdf/2105.00247.pdf Ssnow

Hi, my question regard the possibility to consider a generalization on the product integral (of type II). The product integral is defined in analogy to the definite integral where instead the limit of a sum there is a limit of a product and, instead the multiplication by ##dx## there is the...

It is a good idea!, especially if you consider it came from a young student of the high school ... it seems a laborious method with higher derivatives ... one time I wrote a simple article of the same type involving the Tetration function with application in calculating integrals, it has been...

In mathematics you are able to differentiate single valued-functions and multi-valued functions. https://en.wikipedia.org/wiki/Multivalued_function Ssnow