- #1

- 185

- 16

## Main Question or Discussion Point

at what value of k should the following integral function peak when plotted against k?

[itex]

I_{\ell}(k,k_{i}) \propto k_{i}\int^{\infty}_{0}yj_{\ell}(k_{i}y)dy\int^{y}_{0}\frac{y-x}{x}j_{\ell}(kx)\frac{dx}{k^{2}}

[/itex]

This doesn't look like any orthogonality relationship that I know, it's a 2D integral for starters, but I'm told it should peak at k = k

[itex]

I_{\ell}(k,k_{i}) \propto k_{i}\int^{\infty}_{0}yj_{\ell}(k_{i}y)dy\int^{y}_{0}\frac{y-x}{x}j_{\ell}(kx)\frac{dx}{k^{2}}

[/itex]

This doesn't look like any orthogonality relationship that I know, it's a 2D integral for starters, but I'm told it should peak at k = k

_{i}due to orthogonality of the j_{l}