Gloss function

The brightness function is an empirical relation that determines the distribution of stars by apparent magnitude . Gloss function $A\left(m\right)$ ${\ displaystyle A \ left (m \ right)}$ ${\ displaystyle A \ left (m \ right)}$ determined from the ratio:

$dN\left[m,m+dm\right]=A(m)dm$ ${\ displaystyle dN \ left [m, m + dm \ right] = A (m) dm}$ $dN \ left [m, m + dm \ right] = A (m) dm$

$A(m)={\frac {dN}{dm}}$ ${\ displaystyle A (m) = {\ frac {dN} {dm}}}$ $A (m) = {\ frac {dN} {dm}}$

Where $dN\left[m,m+dm\right]$ ${\ displaystyle dN \ left [m, m + dm \ right]}$ $dN \ left [m, m + dm \ right]$ - the number of stars with visible magnitudes in a given range $\left[m,m+dm\right]$ ${\ displaystyle \ left [m, m + dm \ right]}$ $\ left [m, m + dm \ right]$ , but $m$ ${\ displaystyle m}$ $m$ Is the given apparent magnitude .

Integral Gloss Function - Stars $N\left(m_{max}\right)$ ${\ displaystyle N \ left (m_ {max} \ right)}$ ${\ displaystyle N \ left (m_ {max} \ right)}$ having visible magnitudes not exceeding a given:

$N(m_{max})=\int _{-\infty }^{m_{max}}A(m)dm$ ${\ displaystyle N (m_ {max}) = \ int _ {- \ infty} ^ {m_ {max}} A (m) dm}$ $N (m_ {max}) = \ int _ {- \ infty} ^ {m_ {max}} A (m) dm$

Gloss function

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