wcosmo.taylor.analytic_integral

wcosmo.taylor.analytic_integral(z, Om0, w0=-1, zpower=0)

Compute an integral of the form \(\int_{\infty}^z \frac{(1+z)^k}{E(z)}\) using

\[f(z; \Omega_{m, 0}, w_0) = \int_{\infty}^{z} \frac{dz' (1 + z')^k}{E(z'; \Omega_{m, 0}, w_0)} = \frac{-2\Phi(z; \Omega_{m, 0}, w_0) (1+z)^k } {\sqrt{\Omega_{m, 0}(1 + z)}}.\]

The integral is approximated using the Pade approximation and is up to a factor the term in the braces in (1.1) of Adachi and Kasai.

Parameters:

z: array_like

Redshift

Om0: array_like

The matter density fraction

w0: array_like

The (constant) equation of state parameter for dark energy

Returns:

integral: array_like

The integral of \(1 / E(z)\) from \(\infty\) to \(z\)