# Changes between Version 49 and Version 50 of DatabaseBasedAnalysis/Spectrum

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Timestamp:
Dec 3, 2019, 7:07:57 PM (9 months ago)
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• ## DatabaseBasedAnalysis/Spectrum

 v49 As the simulated energy spectrum is independent of zenith angle, it can be expressed as $dN_0(E,\theta) = N_0\cdot d\eta(E)\cdot d\eta(\theta)$ $dN_0'(E,\theta) = N_0\cdot d\eta(E)\cdot d\eta(\theta)$ with the differential energy spectrum $$\eta(E)$$ and the zenith angle distribution $$\eta(\theta)$$, for the total production range $$E_\textrm{min}$$  to $$E_\textrm{max}$$ and $$\theta_\textrm{min}$$ to $$\theta_\textrm{max}$$ $N_0 = \int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}} dN_0(E,\theta) = N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(E) dE \cdot \eta(\theta) d\theta= N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\eta(E) dE\cdot \int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(\theta) d\theta$ $N_0' = \int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}} dN_0(E,\theta) = N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(E) dE \cdot \eta(\theta) d\theta= N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\eta(E) dE\cdot \int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(\theta) d\theta$ consequently or $N_0 = N_0\cdot \sum_{E_\textrm{min}}^{E_\textrm{max}}\omega_i(E) \cdot \sum_{\theta_\textrm{min}}^{\theta_\textrm{max}}\omega_i(\theta)$ $N_0' = N_0\cdot \sum_{E_\textrm{min}}^{E_\textrm{max}}\omega_i(E) \cdot \sum_{\theta_\textrm{min}}^{\theta_\textrm{max}}\omega_i(\theta)$ with $\sum_{E_\textrm{min}}^{E_\textrm{max}}\omega_i(E) =\sum_{\theta_\textrm{min}}^{\theta_\textrm{max}}\omega_i(\theta) = 1$