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John321
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- TL;DR Summary
- How to write the 3D power spectrum, P(k), as an integral of the angular power spectrum, C_l?
I have the following equation,
$$ C_\ell(z,z') = \int_0^\infty dkk^2 j_\ell(kz)j_\ell(kz')P(k),$$
where $$j_\ell$$ are the spherical Bessel functions.
I would like to invert this relation and write P(k) as a function of C_l. I don't know if this is a well known result, but I couldn't find anything. I've also looked into Fredholm integral equations, but that got me nowhere, and now I'm stuck.
Any ideas on how to tackle this problem?
$$ C_\ell(z,z') = \int_0^\infty dkk^2 j_\ell(kz)j_\ell(kz')P(k),$$
where $$j_\ell$$ are the spherical Bessel functions.
I would like to invert this relation and write P(k) as a function of C_l. I don't know if this is a well known result, but I couldn't find anything. I've also looked into Fredholm integral equations, but that got me nowhere, and now I'm stuck.
Any ideas on how to tackle this problem?
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