- #1

Nabeshin

Science Advisor

- 2,205

- 16

## Main Question or Discussion Point

I have come across the following integral which I need to compute:

[tex]\int_0^{t_1} \int_{\nu_0}^{\infty} \left(\frac{h \nu ^3}{c^2}\right) \frac{1}{e^{\frac{h\nu}{k T(t)}}-1} d\nu dt[/tex]

The problem is, since the inner integral cannot be computed analytically, I have to resort to numerical methods. But, I don't think I can use numerical methods since the inner integral contains the variable t and as such is not purely a function of nu. Any idea how to evaluate something like this?

One thought I had was writing a taylor series for the inner integral treating the time dependent factor as a constant, and just taking the first few terms and proceeding with the integration. This seems rather crude though, so I wonder: is there a better way?

[tex]\int_0^{t_1} \int_{\nu_0}^{\infty} \left(\frac{h \nu ^3}{c^2}\right) \frac{1}{e^{\frac{h\nu}{k T(t)}}-1} d\nu dt[/tex]

The problem is, since the inner integral cannot be computed analytically, I have to resort to numerical methods. But, I don't think I can use numerical methods since the inner integral contains the variable t and as such is not purely a function of nu. Any idea how to evaluate something like this?

One thought I had was writing a taylor series for the inner integral treating the time dependent factor as a constant, and just taking the first few terms and proceeding with the integration. This seems rather crude though, so I wonder: is there a better way?