Changes between Version 134 and Version 135 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/05/19 14:22:07 (6 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -91 +91 @@
 N is the number of events in the energy interval \(E\in[E_\textrm{min};E_\textrm{max}]\) and the zenith angle interval \(\theta\in[\theta_\textrm{min};\theta_\textrm{max}]\)
 
-\[N_0^\textrm{tot} = \sum_{i=0...N}^{E\in[E_\textrm{min};E_\textrm{max}]}\sum_{j=0...N}^{\theta\in[\theta_\textrm{min};\theta_\textrm{max}]} \omega_i(E_i)\cdot \omega_j(\theta_j)\]
+\[N_0^\textrm{tot} = \sum_{i=0...N}^{E\in[E_\textrm{min};E_\textrm{max}]}\sum_{j=0...N}^{\theta\in[\theta_\textrm{min};\theta_\textrm{max}]} \omega(E_i, \theta_j)\]
+
+Since \(\omega(E, \theta) = \omega_E(E)\cdot \omega_\theta(\theta) \)
+
+\[N_0^\textrm{tot} = \sum_{i=0...N}^{E\in[E_\textrm{min};E_\textrm{max}]}\sum_{j=0...N}^{\theta\in[\theta_\textrm{min};\theta_\textrm{max}]} \omega_E(E_i)\cdot\omega_\theta(\theta_j)\]
+
 
 \[N_0^\textrm{tot} = \sum_i^{[E_\textrm{min};E_\textrm{max}]}\sum_j^{[\theta_\textrm{min};\theta_\textrm{max}]} \sum_k^{[\Delta E_i]}\sum_m^{[\Delta \theta_j]} \omega_k(E_k)\cdot \omega_m(\theta_m)\]
 
-\[\omega(E, \theta) = \omega_E(E)\cdot \omega_\theta(\theta) \]