Recent content by teme92

I don't understand how you solved for x. I know normally with an exponential, a natural log would be involved.

If its converted to the wavelength I got. x=\frac{hc}{λkT} 5(e^x-1)=xe^x Which is a similar equation to solve. Where would I go from here?

Homework Statement The Planck blackbody spectrum is given by u(ω,t)=\frac{ħω^3}{π^2c^3(e^{βħω}-1)} Show that the peak of the Planck spectrum for a blackbody at a temperature T occurs at the wavelength λ_{max}T=0.29 where T is in Kelvin and λmax is in cm. Homework Equations...

But do I not want there to be n's in my result?

n=0: a_n = 0 n=1: a_n = \frac{1}{2π} (has zero dividers though) n=2: a_n = \frac{1}{12π}

If I put integers in for n will the result not be a single number?

What would I be checking for?

a_n = \frac{1}{2π}\Big[\frac{(-1)^n}{n-1}-\frac{(-1)^n}{n+1}-\frac{1}{n-1}+\frac{1}{n+1}\Big] Is this correct?

When I sub in and simplify I'm getting: a_n = \frac{1}{2π}\Big[\frac{(-1)^n + (-1)^n}{(n-1)(n+1)}\Big]

I've tried subbing (-1)n in for both of the cos parts but it doesn't simply to what is given.

(-1)^n

-1 for n = odd and 1 for n = even.

Homework Statement I'm calculating the coefficients for the Fourier series and I got to part where I can't simplify an any further but I know I have to. a_n = \frac{1}{2π}\Big[\frac{cos(n-1)π}{n-1}-\frac{cos(n+1)π}{n+1}-\frac{1}{n-1}+\frac{1}{n+1}\Big]Homework EquationsThe Attempt at a...

So I have a long mess of an answer that I won't put up cos it seems pointless. I'm fairly sure it was all differentiated correctly though. For the spherical part do I just start again and change ##z## to ##rcos\theta##?

I know that's the obvious answer but I thought it was to do with what the power was. So I have to differentiate: ##\frac{cz}{(x^2+y^2+z^2)^{\frac{3}{2}}}## With respect to x,y and z?