Recent content by Rulonegger

Homework Statement Prove that \sum_{n=0}^{\infty}{\frac{r^n}{n!}P_{n}(\cos{\theta})}=e^{r\cos{\theta}}J_{0}(r\sin{\theta}) where P_{n}(x) is the n-th legendre polynomial and J_{0}(x) is the first kind Bessel function of order zero. Homework Equations...

Homework Statement If we define \xi=\mu+\sqrt{\mu^2-1}, show that P_{n}(\mu)=\frac{\Gamma(n+\frac{1}{2})}{n!\Gamma(\frac{1}{2})}\xi^{n}\: _2F_1(\frac{1}{2},-n;\frac{1}{2}-n;\xi^{-2}) where P_n is the n-th Legendre polynomial, and _2F_1(a,b;c;x) is the ordinary hypergeometric function...

Correction I'm sorry, but the last expression was Y_{m}(x)=\frac{\cos{m\pi}J_{m}(x)-J_{-m}(x)}{\sin{m\pi}} Any kind of help would be greatly appreciated!

Homework Statement I need to obtain the Bessel functions of the second kind, from the expressions of the Bessel functions of the first kind. Homework Equations Laplace equation in circular cylindrical coordinates reads \nabla^2\phi(\rho,\varphi,z)=0 with...

Thank's TSny, and yeah I've made a copy-paste error. I'm very grateful for your help!

Homework Statement Hello everyone. I need to demonstrate that with a damped free oscillator, which is linear, the total energy is a function of the time, and that the time derivative of the total energy is negative, without saying if the motion is underdamped, critically damped or overdamped...

Oscillation Yeah, i see your comparison, but intuitively i think the motion should be like a sinusoidal function of time, but the period of oscillation is?

Homework Statement A particle with mass m which can move only in one dimension, is subject to a constant force F= \begin{cases}-F_{0} && x>0\\F_{0} && x<0\end{cases} with F_{0}>0. First I've got to say if there is a potential energy. Then i must solve the particle dynamics (i.e. find v(t)...

Thanks jbunniii, you didn't make any error, and you left the problem almost done.

Thanks jbunniii and HallsofIvy. I'm sorry, but I've just made a typing mistake, and I've just copied and pasted the first expression. So, the correct expression to prove is \sum_{n=0}^{\infty}{\frac{(-1)^{n}}{(2n)!}\sum_{k=0}^{2n}{{2n \choose...

Homework Statement I just have to prove the well known identities: \cos(\alpha + \beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta) \sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin( \beta) But the thing is that I've to use the Taylor power series for the sine and cosine...

Thanks haruspex. If i understand, you say that dS=dS_{1}+dS_{2}=\frac{dQ}{T_{1}}+\frac{dQ}{T_{2}}With the fact that T_{1}>T_{2}, therefore a small dQ transferred between them would lead a change in the first entropy which is smaller than the change of the second one, without sayin anything about...

Actually I've used conservation of energy, and i can determine the temperature T of equilibrium, which is T=\frac{N_{1}T_{1}+N_{2}T_{2}}{N_{1}+N_{2}}but when i substitute that expression on the inequality, the later just complicates a little bit more. In despite of this, i think i must...

Homework Statement Hello everyone. My problem is as follows: In a spontaneous process where two bodies at different temperatures T_{1} and T_{2}, where T_{1}>T_{2}, are put together until they reach thermal equilibrium. The number of atoms or molecules of the first is N_{1} and N_{2} for the...