Stellar luminosity functions in the R, I, J, and K bands obtained by transformation from the visual band
The stellar luminosity function that has been measured in the visual band into the R, I, J, and K bands, where it has not yet been obtained directly, is transformed. The transformation is effected by subdividing the total visual function, which includes all stars, into subluminosity functions for each luminosity class (supergiants through white dwarfs), applying the known (V - D) color, D = R, I, J, K for each spectral type, and then summing the resultant transformed subluminosity functions into a total luminosity function for the band D. Simple analytic forms that accurately fit the transformed luminosity functions are given. Consideration is also given to the possibility of a systematic error resulting from the existence of a very red stellar population not accounted for in the visual band luminosity function