Table 7: Calculation of the Schechter function parameter L* and luminosity density $\mathcal{L}$ according to Ajiki et al. (2003) for their sample, our complete sample and the combination of the two. For each sample the luminosity density has been derived from the sum of the candidate luminosities divided by the corresponding survey volume. Then Eq. (2) was solved for L*, with given $\alpha $ and $\phi ^*$ from Ajiki et al. (2003). Finally, the entire luminosity function was integrated to give the final luminosity density.
  $\alpha $ $\log \phi^*$ $\log L^*$ $\log L_{\rm lim}$ log V $\log \mathcal{L}$ Comment
    Mpc-3 erg s-1 erg s-1 Mpc3 erg s-1 Mpc-3  
Case A - - - 42.85 5.26 39.04 Sum of the candidates from Ajiki et al. (2003)
  -1.53 -2.62 42.61 42.85 5.26 39.04 Integrated luminosity function down to Ajiki et al. (2003) survey limit ( $7.0\times10^{42}$ erg s-1)
  -1.53 -2.62 42.61 - - 40.27 Integration of the entire luminosity function
Case B - - - 43.26 5.71 38.36 Sum of the candidates from completeness corrected WFILAS sample
  -1.53 -2.62 42.74 43.26 5.71 38.36 Integrated luminosity function down to the limit of the completeness corrected sample ( $1.8\times10^{43}$ erg s-1)
  -1.53 -2.62 42.74 - - 40.39 Integration of the entire luminosity function
Case C - - - 42.85 5.84 39.19 Sum of the combined WFILAS and Ajiki et al. (2003) samples low luminosity corrections
  -1.53 -2.62 42.66 42.85 5.84 39.19 Integrated luminosity function down to Ajiki et al. (2003) survey limit ( $7.0\times10^{42}$ erg s-1)
  -1.53 -2.62 42.66 - - 40.32 Integration of the entire luminosity function

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