[Aims] We take advantage of the capability of the OTELO survey to obtain the H alpha luminosity function (LF) at z similar to 0.40. Because of the deepest coverage of OTELO, we are able to determine the faint end of the LF, and thus better constrain the star formation rate and the number of galaxies at low luminosities. The AGN contribution to this LF is estimated as well. [Methods] We make use of the multiwavelength catalogue of objects in the field compiled by the OTELO survey, which is unique in terms of minimum flux and equivalent width. We also take advantage of the pseudo-spectra built for each source, which allow the identification of emission lines and the discrimination of different types of objects. [Results] The H alpha luminosity function at z similar to 0.40 is obtained, which extends the current faint end by almost 1 dex, reaching minimal luminosities of log(10) L-lim = 38.5 erg s(-1) (or similar to 0.002 M-circle dot yr(-1)). The AGN contribution to the total H alpha luminosity is estimated. We find that no AGN should be expected below a luminosity of log(10) L = 38.6 erg s(-1). From the sample of non-AGN (presumably, pure SFG) at z similar to 0.40 we estimated a star formation rate density of rho(SFR) = 0.012 +/- 0.005 M-circle dot yr(-1) Mpc(-3).

This work was supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under the grants AYA2013- 46724- P, AYA2014 58861-C3-1- P, AYA2014-58861-C3-2-P, AYA2014-58861-C3-3- P, AYA2016 -75808-R, AYA2016-75931-C2-2-P, AYA2017-88007-C3-1-P, and AYA2017 -88007-C3-2- P. Based on observations made with the Gran Telescopio Canarias installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias, in the island of La Palma. The authors thanks the anonymous referee for her/his feedback and suggestions.