- #1

Bkkkk

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Hey, I have been trying to make Mathematica integrate the following function:

[tex]r_{e}=\frac{c}{H_{0}}\int_{0}^{z}\frac{dz}{\left[\Omega_{NR}(1+z)^{3}+\Omega_n(1+z)^{3-n}+\Omega_{\Lambda}\right]^{\frac{1}{2}}}[/tex]

There are two cases for which this equation needs to be integrated, seperately;

(i) When [tex]\Omega_{\Lambda}=0[/tex]

(ii) [tex]\Omega_n=0 [/tex]

n is real, so is z and the sum of the density parameters is unity, thus if we take case (ii) [tex]\Omega_{\Lambda} = 1 - \Omega_{NR}[/tex]

However Mathematica outputs the formatted version of the input line. Next I thought I would just define a function which includes the above integral, and then plot it for varying values of [tex]\Omega_{NR}[/tex] and n, however the problem is that often times the Kernel crashes or the curves plotted have gaps in them and/or end unexpectedly.

I would of course prefer to have the integrated function as I presume it would save on plotting time as I need make plots for various values of n for case (i).

Thanks

[tex]r_{e}=\frac{c}{H_{0}}\int_{0}^{z}\frac{dz}{\left[\Omega_{NR}(1+z)^{3}+\Omega_n(1+z)^{3-n}+\Omega_{\Lambda}\right]^{\frac{1}{2}}}[/tex]

There are two cases for which this equation needs to be integrated, seperately;

(i) When [tex]\Omega_{\Lambda}=0[/tex]

(ii) [tex]\Omega_n=0 [/tex]

n is real, so is z and the sum of the density parameters is unity, thus if we take case (ii) [tex]\Omega_{\Lambda} = 1 - \Omega_{NR}[/tex]

However Mathematica outputs the formatted version of the input line. Next I thought I would just define a function which includes the above integral, and then plot it for varying values of [tex]\Omega_{NR}[/tex] and n, however the problem is that often times the Kernel crashes or the curves plotted have gaps in them and/or end unexpectedly.

I would of course prefer to have the integrated function as I presume it would save on plotting time as I need make plots for various values of n for case (i).

Thanks

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