From 76f612076ece69650e45cdfdbe1759d5daff2703 Mon Sep 17 00:00:00 2001 From: Yu Feng Date: Sat, 29 Dec 2018 05:56:10 -0800 Subject: [PATCH] Potential typo Looks like the integration bound shall be c on the denominator? --- .../phase_space_models/nfw_profile_source_notes.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source_notes/empirical_models/phase_space_models/nfw_profile_source_notes.rst b/docs/source_notes/empirical_models/phase_space_models/nfw_profile_source_notes.rst index 38a5f7b5d..8332cab26 100644 --- a/docs/source_notes/empirical_models/phase_space_models/nfw_profile_source_notes.rst +++ b/docs/source_notes/empirical_models/phase_space_models/nfw_profile_source_notes.rst @@ -125,7 +125,7 @@ Now we change integration variables :math:`\tilde{r}'\rightarrow c\tilde{r}'=y`: .. math:: - P_{\rm NFW}(<\tilde{r}) = \frac{\int_{0}^{c\tilde{r}}dy\frac{y}{(1 + y)^{2}}}{\int_{0}^{1}dy\frac{y}{(1 + y)^{2}}} + P_{\rm NFW}(<\tilde{r}) = \frac{\int_{0}^{c\tilde{r}}dy\frac{y}{(1 + y)^{2}}}{\int_{0}^{c}dy\frac{y}{(1 + y)^{2}}} and use the definition of :math:`g(x) \equiv {\rm ln}(1+x) - x/(1+x) = \int_{0}^{x}dy\frac{y}{(1+y)^{2}}` to write the above expression as