Recent content by RedDwarf

Let's see if I can do this: If ##\sin(x)/x = 1 - \frac{x^2}{6} + \frac{x^4}{120} +\mathscr O(x^6)##, then $$1/(y+1) = 1-1 + \frac{x^2}{6} - \frac{x^4}{120} +1 + (-\frac{x^2}{6} + \frac{x^4}{120})^2 = 1+\frac{x^2}{6} - \frac{x^4}{120} +\frac{x^4}{36} - 2\frac{x^6}{6*120}+ \frac{x^8}{120})^2$$...

The expansion of ##\sin (x)/x = 1-x^2/3!+x^4/5!-... = \sum (-1)^n \frac{x^{2n}}{(2n+1)!}## The expansion of ## 1/(1+y) = 1-y+y^2-y^3+... = \sum (-1)^n y^n## Then, if I set ##y = \sin (x)/x -1##: ##x/sin(x) = 1- (sin(x)/x-1)+(sin(x)/x-1)^2-(sin(x)/x-1)^3+... =3-sin(x)/x + sin^2(x)/x^2- 2sin(x)/x...

Hey everyone 1. Homework Statement I want to compute the Taylor expansion (the first four terms) of $$f(x) =x/sin(ax)$$ around $$x_0 = 0$$. I am working in the space of complex numbers here. Homework Equations function: $$f(x) = \frac{x}{\sin (ax)}$$ Taylor expansion: $$ f(x) = \sum...

Ah, now I know where this is going, thanks! The Fourier transform of the derivative of a general function is related to the function like so: ## \hat{g'}(x) = ip \hat{g}(x) ##. In my case this would mean that I can look at the Fourier transform of the derivative, divided by ip: ##\hat{f}(x) =...

The function is the derivative of the primitive function ##\frac{d}{dx} F(x) = f(x)## Yet, I am not sure how this is helping me in this Fourier transform (sorry, I'm a bit slow today)

This is what I think as well. If they meant the primitive function though, how could I solve it then?

Homework Statement I am supposed to compute the Fourier transform of f(x) = integral (e-a|x|) Homework Equations Fourier transformation: F(p) = 1/(2π) n/2 integral(f(x) e-ipx dx) from -infinity to +infinity The Attempt at a Solution My problem is, that I do not know how to handle that there...

Thank you, this helped very much!

Thank you so much, this is exactly what my tired brain couldn't put into words!

Hey! I was reading some script and when it comes to the cosmological redshift, it says, that only relativistic particles are affected by cosmological redshift. This does feel quite natural, however, I haven't been able to come up with an explanation that shows it with proper physics and...

Hey guys! I'm an undergrad student in physics hoping to have interesting conversations and to find answers to my many, many questions :) Cheers, Max