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YinZhe Ma
Joined: 09 Oct 2008 Posts: 11 Affiliation: University of KwaZuluNatal

Posted: July 31 2017 


I am looking at the Antony Lewis' paper
https://arxiv.org/pdf/0804.3865.pdf
for Eq.(B3) on page 11, there is this equation of number of free electron per hydrogen atom.
But for this equation, if z→ large values, then y=(1+z)^{3}/2 will also become large values, while y(z_{re}) and Δ_{y} are fixed. Since "tanh(x→∞)→1", then for large redshift, x_{e}→1.
If z→0, then tanh function will becomes a negative value but greater than −1, then x_{e}→0.
So this is completely opposite to the trend of Fig.6 on the same page. Can anyone explain what is going on here?
Perhaps I made some stupid mistake, please point it out. Thank you. 

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Antony Lewis
Joined: 23 Sep 2004 Posts: 1278 Affiliation: University of Sussex


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YinZhe Ma
Joined: 09 Oct 2008 Posts: 11 Affiliation: University of KwaZuluNatal

Posted: July 31 2017 


Oh, then this typo affects the Planck reionization paper, the published version of Planck intermediate results XLVII. Planck constraints on reionization history,
page 5, equation 2
also takes this typo. 

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